UC-NRLF 


SB    Sfi7    3m 


THE 

Elements  of  Navigation 

A    short   and   complete   explanation   of  the 
standard  methods  of  finding  the  posi- 
tion of  a  ship  at  sea  and  the 
course   to    be   steered 

DESIGNED   FOR 

THE   INSTRUCTION   OF   BEGINNERS 
NEW   EDITION 

BY 
W.  J.  HENDERSON,  A.M. 

LIEUTENANT  IN  THE  FIRST  NAVAL  BATTALION  OF 
NEW   YORK 

Illustrated 


NEW    YORK   AND    LONDON 
HARPER  &   BROTHERS  PUBLISHERS 


HS* 


BOOKS  BY 
W.  J.  HENDERSON 


AFLOAT    WITH    THE    FLAG 

Illustrated.     Post  8vo,  Cloth, 
SEA  YARNS   FOR   BOYS,  SPUN  BY  AN  OLD  SALT 

Illustrated.     Post  8vo,  Cloth,    : 


HARPER  &  BROTHERS,  NEW  YORK 


ELEMENTS  OF  NAVIGATION 


Copyright,  1895,  1917,  by  Harper  &  Brothers 

Printed  in  the  United  States  of  America 

Published  May,  1917 

E-R 


TO 

CAPTAIN  J.  W.  MILLER 

COMMANDING   THB  NAVAL   MILITIA 
NEW   YORK 


362253 


PUBLISHERS*   INTRODUCTION 
TO  NEW  EDITION 

THE  history  of  the  three  years  1.914  to  1917 
has  been  made  with  astounding  rapidity  and 
no  part  of  it  has  been  more  absorbing  than 
that  dealing  with  naval  operations.  The 
position  of  our  own  country  in  the  beginning 
of  the  great  European  war  seemed  to  the 
casual  observer  to  be  one  of  perfect  security. 
We  had  three  thousand  miles  of  ocean  between 
us  and  the  warring  nations,  and  aH  we  had  to 
do  was  to  mind  our  own  business  and  nothing 
could  happen  to  us. 

But  it  slowly  dawned  upon  all  minds  that 
unless  we  were  disposed  to  mind  our  own 
business  by  withdrawing  from  the  Atlantic 
Ocean  and  making  no  attempt  to  send  our 
ships  into  European  ports,  we  should  presently 
be  forced  either  to  defend  our  rights  or  to 
admit  that  we  did  not  have  any. 

The  nature  of  the  naval  warfare  developed 
by  the  skill  and  daring  of  the  Germans — to 
take  no  account  of  the  lawlessness  of  it — 
compelled  England  to  invent  novel  and  ex- 
citing measures  of  defense.  The  submarine 


vessel  was  not  new:  all  nations  were  ac- 
quainted with  it.  But  it  had  been  regarded 
as  a  weapon  of  offense  against  battle-ships 
and  cruisers. 

When  Germany  disclosed  her  policy  of 
building  these  craft  in  large  numbers  and 
using  them  for  the  destruction  of  merchant- 
men, the  world  suddenly  learned  that  a  new 
type  of  commerce-destroyer  had  come  into 
existence  and  that  new  methods  of  safeguard- 
ing the  cargo-carriers  must  be  devised.  The 
British  coasts  are  surrounded  by  a  cordon 
of  trawlers  used  in  mine-sweeping  and  motor 
vessels  designed  and  operated  as  submarine- 
chasers. 

In  the  summer  of  1916  the  Germans  sent 
to  the  United  States  a  commercial  submarine 
called  the  Deutschland.  She  made  two  voy- 
ages, once  landing  at  Norfolk  and  once  at 
New  London.  We  are  told  that  she  was  the 
avant-courier  of  a  fleet  of  submarine  cargo- 
carriers  whose  only  purpose  was  to  restore 
commercial  intercourse  with  this  country, 
made  impossible  for  surface  ships  by  the 
British  blockade. 

As  the  relations  between  the  United  States 
and  Germany  became  more  and  more  difficult 
because  of  the  deaths  of  American  citizens  on 
peaceful  merchantmen  sunk  by  German  sub- 


vfl 


marines,  the  German  Government  deemed  it 
wise  to  give  us  a  gentle  hint  of  what  might 
happen  to  us  if  we  did  not  behave  with  the 
greatest  discretion.  Accordingly,  U-boat  53, 
a  war-vessel,  suddenly  arrived  in  Newport, 
and  after  a  brief  stay  put  to  sea  again,  where 
she  promptly  sank  several  ships  close  aboard 
of  our  coast  and  forced  us  to  send  our  naval 
craft  to  rescue  the  passengers  and  crews. 

Before  this  naval  officers  had  known  well 
that  it  was  our  duty  to  prepare  for  trouble. 
But  even  this  incident  did  not  serve  to  arouse 
the  people  at  large,  and  the  beginning  of  our 
war  with  Germany  found  us  struggling  to 
develop  overnight  an  adequate  fleet  of  small 
patrol  and  guard  vessels  to  protect  our 
coasts  and  our  shipping  from  the  attacks  of 
German  sea  raiders  or  the  more  dreaded 
submarine. 

The  Navy  League  contributed  much  to  the 
spread  of  information  on  this  vital  subject  and 
the  newspapers  published  pictures  of  the  type 
of  motor-launches  (as  they  are  called)  de- 
signed by  Great  Britain.  These  are  vessels 
in  the  neighborhood  of  one  hundred  feet  in 
length  and  of  very  light  draught.  They  offer 
no  target  for  torpedoes,  and  the  submarine 
(not  submerged)  which  meets  one  must  de- 
pend on  her  shell  fire. 


vlH 


Furthermore,  these  vessels  are  very  quickly 
built,  are  very  speedy,  and  can  outmanceuver 
a  submarine.  The  development  of  the  marine 
motor  in  recent  years  has  of  course  made 
these  vessels  a  possibility  and  placed  the 
handling  of  their  machinery  within  the  reach 
of  all  kinds  of  men.  Here,  then,  is  an  op- 
portunity for  service  awaiting  every  yachts- 
man and  fisherman. 

One  officer  and  a  very  small  crew,  contain- 
ing at  least  one  expert  gunner,  is  required  for 
each  boat.  Since  the  work  will  be  exceed- 
ingly rough,  up  and  down  the  coast,  close 
inshore,  or  well  off  in  all  kinds  of  weather, 
day  and  night,  the  officers  will  need  to  be 
navigators  possessed  of  ready  knowledge  and 
resource. 

This  book,  which  was  designed  originally 
for  the  benefit  of  naval-militia  officers  and 
yachtsmen,  ought  to  find  a  welcome  among 
men  who  are  preparing  for  the  coast  service. 
If  for  no  other  reason,  the  volume  should  be 
desirable  because,  while  it  is  of  most  conven- 
ient size,  it  contains  the  whole  science  '  of 
practical  navigation. 

The  book  has  stood  the  test  of  more  than 
twenty  years.  It  is  more  popular  to-day 
than  in  its  earliest  seasons.  When  it  was 
first  published  the  Navy  Department  imme- 


diately  placed  it  on  the  list  of  works  recom- 
mended for  use  by  the  naval  militia  and 
took  a  number  of  copies  which  were  distrib- 
uted among  the  various  organizations  in  order 
to  introduce  it.  Since  that  time  the  work 
has  had  continual  favor  among  naval  militia- 
men preparing  for  examinations  as  officers. 

When  the  war  with  Spain  began  a  large 
number  of  officers  of  the  Navy  who  had  re- 
signed, but  wished  to  volunteer,  used  this 
book  as  the  most  suitable  for  a  quick  and 
firm  recovery  of  their  knowledge  of  naviga- 
tion. As  one  of  them  said  to  the  author,  "I 
could  never  have  got  back  into  the  service 
if  it  had  not  been  for  your  book." 

Yachtsmen  also  have  found  this  al  conven- 
ient treatise  for  their  purposes  and  many  of 
them  have  testified  as  to  its  value. 

Not  a  few  master  mariners,  captains  of 
vessels  trading  in  foreign  ports,  have  taken 
the  book  up  and  keep  it  in  their  cabins  be- 
cause of  its  compact  presentation  of  all  es- 
sential formulae. 

The  work  has  thus  had  approval  which  has 
been  extremely  gratifying  to  the  publishers 
and  the  author.  The  present  time  offers  the 
widest  field  of  usefulness  for  such  a  volume, 
and  this  new  edition  has  been  prepared  to 
meet  the  conditions. 


Additions  covering  the  organization  and 
manning  of  the  Naval  Coast  Defense  Reserve 
and  subjects  connected  with  navigation  which 
should  be  known  by  its  officers  have  been 
made.  Hints  about  practical  methods  of 
coastwise  navigation  under  war-time  condi- 
tions, suggestions  as  to  the  study  of  coast  sky- 
lines, the  furthest  development  of  the  use  of 
compass  and  lead  in  the  blind  work  of  un- 
lighted  nights  or  fogs,  and  the  inestimable 
value  of  lines  of  bearing  in  sailing  along  a 
coast  have  been  added  by  the  author,  who 
has  sought  to  give  them  the  directness, 
brevity,  and  completeness  of  the  older  por- 
tions of  the  book. 

The  publishers  hope  that  in  its  new  form 
this  volume  will  prove  of  increased  usefulness. 


PREFACE 

THE  need  of  a  short,  simple,  and  yet 
comprehensive  book  on  the  art  of  navi- 
gating a  ship  has  led  the  author  to  under- 
take the  preparation  of  the  present  work. 
The  extant  treatises  on  the  subject  are  of 
two  kinds :  first,  introductory  and  simple, 
but  incomplete ;  and,  second,  exhaustive, 
but  incomprehensible  to  the  beginner.  The 
aim  of  this  book  is  to  instruct  the  begin- 
ner, leading  him  step  by  step  from  the  first 
operations  to  the  perfection  of  the  art  as 
found  in  the  Sumner  method.  The  in- 
structions have  been  made  as  terse  as 
possible,  and  yet  the  author  believes  that 
clearness  has  not  been  sacrificed.  Funda- 
mental principles  have  been  explained,  but 
no  attempt  has  been  made  to  elucidate  the 
higher  mathematics  of  the  subject.  Stu- 
dents who  have  tried  to  learn  navigation 
from  books  like  Captain  Lecky's  inimitable 
Wrinkles  in  Practical  Navigation,  which 
is  addressed  to  navigators  only,  or  from 


xii 


Bowd itch's  American  Navigator,  which  is 
only  for  mathematicians,  will,  it  is  hoped, 
appreciate  this  little  book.  The  explana- 
tions of  the  uses  of  the  tables  and  the  Nau- 
tical Almanac  are  a  new  feature  in  a  work 
of  this  kind. 

The  author  has  consulted  the  following 
authorities :  Bowd  itch's  American  Navi- 
gator, Norie's  Epitome  of  Navigation, 
Raper's  Practice  of  Navigation,  Lieutenant 
Sturdy 's  Practical  Aid  to  the  Navigator, 
Lecky's  Wrinkles  in  Practical  Navigation, 
Qual trough's  Sailor's  Handy  Book,  Patter- 
son's Navigator  s  Pocket  Book,  Proctor's 
Half  Hours  with  the  Stars,  and  Towson's 
Deviation  of  the  Compass.  He  desires  to 
express  his  indebtedness  to  all  of  these 
works,  but  most  especially  to  those  of  Cap- 
tain Lecky  and  Lieutenant  Sturdy. 


CONTENTS 


PAGE 

PUBLISHERS'  INTRODUCTION  .......   v 

PREFACE        ...........  Zi 

INTRODUCTION     .....       ,....! 

VARIATION  ...........  ii 

DEVIATION      ...........  14 

HOW  TO  FIND  THE  DEVIATION      .....  19 

LEEWAY   .        .        ..........  83 

THE  LOG      .....               .....  26 

THE  LEAD-LINE   ..........  32 

CHARTS         ...........  34 

CHART  SAILING    .........        .  4» 

DEAD-RECKONING  .........  48 

EXAMPLES  FOR  PRACTICE     .......  59 

WORKING  A  TRAVERSE       .......  60 

HOVE  TO  ............  65 

SHAPING  THE  COURSE         .......  «6 

NAVIGATION  BY  OBSERVATION  ......  70 

SEXTANT  ADJUSTMENTS     .......  75 

INDEX  ERROR       ..........  77 

HINTS  ON  TAKING  ALTITUDES       .....  78 

CORRECTING  THE  ALTITUDE       .....        .79 

THE  CHRONOMETER     ........  83 

THE  NAUTICAL  ALMANAC       .......  85 

APPARENT  AND  MEAN  TIME-THE  EQUATION      .        .  92 

LATITUDE  BY  MERIDIAN  ALTITUDE     ....  94 

LATITUDE  BY  MERIDIAN  ALTITUDE  OF  A  STAR  .  102 

LATITUDE  BY  MERIDIAN  ALTITUDE  OF  A  PLANET  .  107 


«v 

PACK 

LATITUDE  BY  MERIDIAN  ALTITUDE  OF  THE  MOON  108 
MERIDIAN  ALTITUDE  BELOW  THE  POLE  .  .  .no 
LATITUDE  BY  EX-MERIDIAN  ALTITUDE  OF  THE  SUN  113 
LATITUDE  BY  THE  POLESTAR  ....  .1*3 

COMPASS  ERROR  BY  AZIMUTHS 133 

LONGITUDE  BY  CHRONOMETER  (OR  TIME)  SIGHT    .  134 

REMARKS  ON  LONGITUDE 141 

LONGITUDE  BY  SUNRISE  AND  SUNSET  SIGHTS  .  .  143 
CHRONOMETER  SIGHT  OF  A  STAR  .  .  .  .  M4 

SUMNER'S  METHOD     .        .        .        .     ' 149 

EXAMPLE  OF  SUMNER'S  METHOD  WITH  THE  SUN  165 
EXAMPLE  OF  SUMNER  LINES  WITH  TWO  STARS  .  170 

GREAT-CIRCLE  SAILING 173 

DISTANCE  AND  DANGER  ANGLES 178 

ALLOWANCE  FOR  TIDES 184 

KEEPING  THE  LOG 185 

RATING  A  CHRONOMETER 189 

CARE  OF  A  CHRONOMETER 192 

HINTS  ON  CONDUCTING  VOYAGES  ....  195 
EXAMPLES  FOR  PRACTICE : 

DEAD-RECKONING 198 

SHAPING  COURSE  BY  MERCATOR'S  SAILING  .  199 
LATITUDE  BY  MERIDIAN  ALTITUDE  OF  SUN  .  199 
LATITUDE  BY  MERIDIAN  ALTITUDE  OF  STAR.  200 
LATITUDE  BY  MERIDIAN  ALTITUDE  BELOW  THE 

POLE aoi 

LATITUDE  BY  EX-MERIDIAN  ALTITUDES    .        .       aoi 

LATITUDE  BY  THE  POLESTAR 202 

LONGITUDE  BY  CHRONOMETER  SIGHT       .        .       202 

WAR-TIME  PROBLEMS 204 

THE  NAVAL  COAST-DEFENSE  RESERVE  ....       216 


ELEMENTS  OF  NAVIGATION 


THE  reader  of  this  book  is  cautioned 
that  no  words  are  wasted  in  it.  Facts  are 
stated  once  and  not  repeated.  Explana- 
tions are  given  but  once.  The  student 
must  master  each  fact,  each  explanation, 
and  each  process  before  proceeding  to  the 
next. 

The  books  and  instruments  needed  in 
the  study  of  navigation  are  mentioned  in 
the  proper  places.  The  beginner,  having 
mastered  this  book,  will  be  prepared  to  en- 
ter upon  the  actual  practice  of  navigation, 
but  will  naturally  have  much  to  acquire 
from  experience. 

A  navigator's  library  should  contain  such 
works  as  those  mentioned  in  the  Preface, 
and  also  treatises  on  the  waters  to  be  navi- 
gated, such  as  the  American  Coast  Pilot, 
Findlay's  North  and  South  Atlantic,  and 
others. 


A  complete  list  and  description  of  all 
lights  and  beacons  on  the  Atlantic  and 
Gulf  coasts  of  the  United  States  can  be 
obtained  at  any  nautical-instrument  house 
free. 

The  Nautical  Almanac  can  be  purchased 
for  50  cents. 

It  is  presumed  that  the  student  knows 
what  latitude  and  longitude  are,  and  that 
he  can  add,  subtract,  multiply,  and  divide 
degrees,  minutes,  and  seconds,  and  hours, 
minutes,  and  seconds,  and  can  work  with 
decimal  fractions. 


Navigation  is  the  art  of  finding  the  geo- 
graphical location  of  a  vessel  at  sea,  the 
most  direct  course  to  be  steered  in  pursuit 
of  the  voyage,  and  the  distance  to  be  made. 

There  are  two  branches  of  the  art — 
dead-reckoning  and  observation. 

Navigation  by  dead-reckoning  consists 
in  actually  measuring  the  courses  and  dis- 
tances sailed  by  the  ship,  and  from  them 
computing  the  distance  and  direction  from 
the  port  left  and  to  the  port  sought. 

Navigation  by  observation  consists  in 
measuring  the  angular  altitude  of  celestial 
bodies  above  the  horizon,  and  computing 


the  position  of  the  ship  by  the  application 
of  astronomical  and  mathematical  laws. 

The  problems  of  dead  -  reckoning  are 
solved  by  plane  trigonometry ;  those  of  ob- 
servation by  spherical  trigonometry.  But 
as  the  trigonometrical  data  are  all  pro- 
vided in  the  tables  printed  in  epitomes  of 
navigation,  the  mariner  is  not  required  to 
be  acquainted  with  any  higher  mathemat- 
ics than  simple  arithmetic. 

The  instruments  used  in  dead-reckoning 
are  the  compass,  log,  and  lead-line.  The 
compass  shows  the  direction  in  which  the 
ship  is  travelling;  the  log  measures  the 
speed  or  the  distance.  The  lead' is  used 
when  on  soundings  to  measure  the  depth 
of  water  and  ascertain  the  character  of  the 
bottom.  These  data,  referred  to  the  chart, 
throw  valuable  light  on  the  question  of  the 
ship's  position.  Approaching  a  coast  in 
thick  weather,  or  on  a  dark,  cloudy  night, 
the  lead  is  the  navigator's  main  reli- 
ance. 

In  addition  to  these  instruments,  the 
navigator  requires  for  all  his  work  accurate 
charts  of  the  waters  which  he  is  traversing 
and  their  coasts.  Charts  issued  by  gov- 
ernments are  rnore  trustworthy  than  those 


COMPASS-CARD,  SHOWING   POINTS   AND   DEGREES 

published  by  private  firms,  which  have  not 
the  resources  of  nations. 

The  mariner's  compass  is  the  first  in- 
strument which  the  navigator  must  know. 
It  is  presumed  that  any  person  who  reads 
this  book  has  seen  a  compass  ;  therefore 
it  is  not  described.  The  card  is  the  part 
which  concerns  the  learner  at  this  point. 
Its  circumference  is  divided  into  32  equal 
parts,  called  points.  Each  point  has  a 


name,  and  these  names  the  student  must 
learn  to  repeat  in  regular  order  from  north 
around  by  way  of  east  and  back  to  north, 
thus: 

North,  north-by-east,  north  -  northeast, 
northeast-by-north,  northeast,  northeast- 
by-east,  east-northeast,  east-by-north,  east, 
east-by-south,  east-southeast,  southeast-by- 
east,  southeast,  southeast-by-south,  south  - 
southeast,  south-by-east,  south,  south-by- 
west,  south-southwest,  southwest-by-south, 
southwest,  southwest-by-west,  west-south- 
west, west-by-south,  west,  west-by-north, 
west-northwest,  northwest-by-west,  north- 
west, north  west-by-north,  north-northwest, 
north-by-west,  north. 

This  is  called  "  boxing  the  compass." 
Any  intelligent  person  can  easily  discover 
the  system  on  which  the  points  are  named. 
North,  south,  east,  and  west  are  called  the 
cardinal  points;  northeast, southeast,south- 
west,  and  northwest  are  the  intercardinal 
points.  Each  cardinal  point  is  8  points 
away  from  the  nearest  cardinal,  and  4 
points  away  from  the  nearest  intercar- 
dinal. 

In  navigation  all  courses  are  reckoned 
from  the  north-and-south  line  of  the  com- 


pass,  which  is  called  the  meridian.  Thus 
north  -  northeast,  south  -  southeast,  north- 
northwest,  and  south-southwest  are  2-point 
courses.  East  and  west  are  8-point  courses. 

TABLES  SHOWING   THE    NAMES  OF  POINTS   AND  QUARTER- 
BACH   COURSE,    AND    THE    ANGLE    MADE    BY   EACH    WITH 


North 

Points 

N.*E. 

N.&fW. 

X 

2°  48  45 

N.#E. 

N.*W. 

% 

5°  37  30 

N.XB. 

N.#W. 

X 

8°  26'  15" 

N.-by-E. 

N.-by-W. 

n°  15'  - 

N.-by-E.^E. 
N.-by-E.  #E. 

N.-by-W.^W. 
N.-by-W.^W. 

l* 

iX 

14°  3  45'; 
16°  52'  3° 

N.-by-E.^E. 

N.-by-W.  %W. 

1% 

i9°  4''  '5" 

N.N.E. 

N.N.W. 

2 

22°  30'  — 

N.N.E.&E. 

N.N.W.tfW. 

2^ 

25°  i»'  45" 

N.N.E.^E. 

N.N.W.^W. 

2^ 

28°  73°; 

N.N.E.^E. 

N.N.W.XW. 

2^ 

30°  56  '5 

N.E.-by-N. 

N.W.-by-N. 

3 

33°  45'  - 

N.E.^N. 

N.W.^N. 

3^ 

36°  33,  45  ' 

N.E.^N. 

N.W.^N. 

3^ 

39°  22  30 

N.E.^N. 

N.W.^N. 

3% 

42°  «'  15' 

N.E. 

N.W. 

4 

45°  

N.E.#E. 

N.W.^W. 

4¥ 

47°  48;  45'' 

N.E.#E. 

N.W.^W. 

4M 

50°  37  30  ' 

N.E.%E. 

N.W.^W. 

4^ 

53°  26'  15" 

N.E.-by-E. 

N.W.-by-W. 

5 

56°  15  - 

N.E.-by-E.#E. 
N.E.-by-E.  ^E. 

N.W.-by-W.^W. 
N.W.-by-W.  MW. 

5* 
5M 

59°  3'  45" 
61°  52'  30" 

N.E.-by-E.&E. 
E.N.E. 

N.W.-by-W.  %W. 
W.N.W. 

5^ 
6 

64°  41;  IS" 
67°  3°  — 

E.N.E.^E. 

W.N.W.^W. 

6^ 

70°  1  8'  45" 

E.N.E.^E. 

W.N.W.^W. 

6* 

73   7  3°  ' 

E.N.E.&E. 

W.N.W.^W. 

6^ 

75°  56'  15 

E.-by-N. 

W.-by-N. 

7 

78°  45'  - 

E.XN. 

W.XH, 

73^ 

81°  33  45  ' 

E.^N. 

W.^N. 

7^ 

84°  22'  30'' 

E.#N. 

W.^N. 

7X 

87°  n'  15" 

East. 

West. 

8 

90°  

Southeast -by -south  is  a  3-point  course. 
The  student  should  examine  the  compass 
card  and  see  how  many  courses  of  each 
kind  there  are,  bearing  in  mind  that  there 

POINTS,  NUMBER  OF  POINTS  AND  FRACTIONS  OF  POINTS  IN 
THE  MERIDIAN. 


South 

Points 

SjfE. 

s.^w. 

^ 

2°  48'  45" 

S.^W. 

xi" 

5°  37'  3o" 

S.%E. 

s.  %w. 

% 

8°  26'  15" 

S.-by-E. 

S.-by-W. 

i 

.1°  15'  - 

S.-bv-E.^E. 
S.-by-E.  J£E. 

S.-by-W.^W. 
S.-by-W.^W. 

\% 

'4°     3;  45,' 
16°  52'  30" 

S.-by-E.%E. 

S.-by-W.%W. 

*% 

19°  41'  15" 

S.S.E. 

S.S.W. 

2 

22°    30'   — 

S.S.E.&E. 

S.S.W.^W. 

25°  18'  45" 

S.S.E.^E. 

s.s.w.^w. 

2)£ 

28°      /   30" 

S.S.E.^E. 

s.s.w.^w. 

2% 

30°  56'  15" 

S.  E.-by-S. 

S.W.-by-S. 

33°  45'  — 

S.E.^S. 

s.w.^s. 

3x^ 

36°  33'  45 

S.E.^S. 

s.w.^s. 

3^ 

39°  22    30" 

o.  ll>.  74  o. 

s.w.^s. 

3% 

42°  ii     15" 

S.E. 

s.w. 

4 

45°  

S.E.^E. 

s.w.^w. 

4# 

47°  48;  45" 

S.E.^E. 

s.w.^w. 

4^ 

50°  37    30 

S.E.^E. 

s.w.%w. 

4^ 

53°  26'  is" 

S.E.-by-E. 

S.W.-by-W. 

5 

56°  IS'  — 

S.E.-by-E.^E. 

S.W.-by-W.^W. 

5# 

59°     3'  45" 

S.E.-by-E.^E. 

S.W.-by-W.  >£W. 

5^ 

61°  52'  30" 

S.E.-by-E.  %E. 

S.W.-by-W.^W. 

64°  4i'  IS" 

E.S.E. 

W.S.W. 

6* 

67°  30'  - 

E.S  E  3^E. 

W.S.W.^W. 

6^" 

70°  1  8'  45" 

E.S.'E.^E. 

w.s.w.^w. 

6^ 

73°     7    3o" 

E.S.E.^E- 

w.s.w.^w. 

6% 

75°  56'   15" 

E.-by-S. 

W.-by-S. 

7 

78°  45'  - 

E.&S. 

w  %s 

7% 

81°  33'  45 

E.^S. 

w^s. 

7% 

84°  22'  30" 

w.^s. 

7% 

87°  ii'  15" 

East.' 

West. 

8 

90°  

is  nothing  greater  than  an  8-point  course. 
After  a  careful  study  of  the  points  the  stu- 
dent should  be  able  to  answer  with  facility 
all  such  questions  as  these  : 

How  many  i -point  courses  are  there? 
2-point?  3-point,  etc.  ?  Name  them.  How 
many  points  is  it  from  E.S.E.  to  S.W.-by- 
S.  ?  How  many  points  from  N.E.-by-E.  to 
W.-by-S.  ?  How  many  points  from  E.-by- 
S.  to  E.N.E.?  What  points  are  3  points 
away  from  W.-by-N.  ? 

Again,  a  square-rigged  vessel  beating  to 
windward  will  sail  a  course  6  points  off 
the  wind.  The  navigator  must  be  able  to 
answer  all  such  questions  as  these :  Head- 
ing N.N.E.  on  the  port  tack,  how  will  the 
vessel  head  when  she  has  come  about? 
(The  answer  will  require  a  count  of  12 
points.)  Ship  heading  S.-by-W.  close  haul- 
ed on  the  starboard  tack,  what  direction  is 
the  wind  ? 

Until  the  student  is  master  of  the  points 
of  the  compass  and  their  relations  he 
should  go  no  further.  When  he  has  learned 
them,  he  must  acquaint  himself  with  the 
half  and  quarter  points  as  set  forth  in  the 
preceding  table. 

The  next  step  is  to  learn  the  angle  which 


each  course  makes  with  the  meridian. 
Meridians  are  imaginary  lines  running 
north  and  south  from  pole  to  pole  and 
used  for  the  determination  of  longitude. 
The  meridian  of  the  compass  is  so  called 
because  it  is  the  north-and-south  line,  and 
may  be  regarded  as  coinciding  with  the 
imaginary  meridian  on  which  the  ship  is 
located.  If  an  actual  north-and-south  line 
were  ruled  on  the  surface  of  the  sea,  and 
you  started  your  ship  off  to  the  northeast, 
you  would  at  once  see  that  she  was  sailing 
on  a  course  that  made  an  angle  of  45°  from 
the  meridian.  But  your  compass  will  tell 
you  the  same  thing. 

The  circumferences  of  all  circles,  no  mat- 
ter how  large  or  how  small,  are  divided  into 
360  equal  parts  called  degrees,  and  all  an- 
gles are  measured  by  these.  A  single 
glance  at  the  accompanying  diagram  will 
illustrate  this.  The  angles  at  a  do  not 
increase  in  size  because  their  boundary 
lines  are  prolonged.  If  these  lines  were 
prolonged  till  they  reached  the  apparent 
sky  the  angle  at  their  juncture  would  be 
the  same  size— 45°.  A  degree,  therefore, 
is  ^J^  of  the  circumference  of  any  circle, 
no  matter  what  size.  Do  not  forget  this 


important  fact.  If  you  divide  the  360°  of 
the  compass-card  by  its  32  points,  you  will 
learn  that  i  point 
equals  11°  15'.  By 
adding  11°  15'  for 
each  additional 
point,  you  will  learn 
that  2  points  equal 
22°  30',  3  points  33° 
45',  4  points  45°,  5 
points  56°  i  5',  6 
points  67°  30',  7 
points  78°  45',  and  8 
points  90°.  Sailing- 
vessels  cannot  be  steered  closer  than  a 
quarter  of  a  point,  and  for  their  naviga- 
tion a  quarter  -  point  may  be  roughly  es- 
timated as  3°.  Steamers  can  be  steered 
more  closely,  and  their  courses  are  set  in 
degrees.  A  course  of  this  kind  is  ex- 
pressed as  so  many  degrees  east  or  west 
from  the  meridian,  thus:  N.  47°  E.,  S« 
36°  W. 


QUARTER-CIRCLE 


VARIATION 

The  north  point  of  the  compass  indi- 
cates true  or  geographical  north  at  only  a 
few  places  on  the  globe.  At  all  other 
places  it  points  a  little  to  one  side  or  the 
other  of  north.  This  error  is  called  varia- 
tion of  the  compass. 

It  is  caused  by  the  fact  that  the  mag- 
netic north  and  south  poles  of  the  earth 
do  not  coincide  with  the  true  or  geographi- 
cal poles.  The  former  is  several  hundred 
miles  south  of  the  geographical  pole,  and 
the  latter  several  hundred  miles  north. 
The  needle  is  perfectly  true ;  it  points  right 
at  the  magnetic  north  pole.  But  that  pole 
is  not  the  north  end  of  the  earth's  axis. 

In  navigating  a  vessel  it  is  necessary  to 
make  allowance  for  this  variation.  The 
amount  of  allowance  and  its  direction  are 
indicated  on  the  charts.  On  large  charts, 
such  as  that  of  the  North  Atlantic,  will  be 
found  irregular  lines  running  from  the  top 
to  the  bottom  of  the  paper,  and  having  be- 
side them  such  inscriptions  as  10°  W.,  15° 
W.  This  means  that  along  this  line  the 
variation  of  the  compass  from  true  north 
is  10°  W.,  15°  W.  There  are  certain  lines 


which  have  no  variation,  and  here  no  al- 
lowance is  to  be  made.  On  small  charts, 
such  as  that  of  New  York  Bay,  the  varia- 
tion is  shown  by  the  compass-card  printed 
on  the  chart.  The  north  point  of  it  will 
be  found  slewed  a  little  to  the  eastward  or 
westward  of  a  meridian  line,  and  near  it 
will  be  seen  an  inscription,  such  as  "  Varia- 
tion 11°  W.  in  1892."  Now  let  us  see  how 
this  variation  affects  the  compass  aboard 
ship,  and  how  we  are  to  allow  for  it,  so  that 
we  shall  know  exactly  which  way  we  are 
going,  even  when  the  compass  does  not  tell 
the  truth. 

Let  the  outer  circle  represent  the  sea 
horizon,  the  inner  circle  the  compass-card. 
The  variation  is  one  point  westerly.  Hence 
the  north  point  of  the  compass  points  to 
the  north-by-west  point  of  the  horizon,  and 
the  south  point  of  the  compass  to  the 
south  -  by  -  east  point  of  the  horizon.  In 
other  words,  standing  at  the  centre  and 
looking  towards  the  circumference,  you 
find  that  every  point  on  the  compass  is 
one  point  to  the  left  of  the  proper  place. 
If  your  compass  says  you  are  sailing  north, 
you  are  really  sailing  N.-by-W.  If  it  says 
south,  you  are  going  S.-by-E.  If  it  says 


True  North 


TrueSoufh 

VARIATION  OF  COMPASS 

east,  you  are  going  E.-by-N.  Hence  we 
get  these  rules : 

To  correct  a  compass  course. — When  the 
variation  is  westerly,  the  true  course  will 
be  as  many  points  to  the  left  of  the  com- 
pass course  as  there  are  points  of  variation. 
When  the  variation  is  easterly,  the  true 
course  will  be  as  many  points  to  the  right 
of  the  compass  course. 

Conversely,  having  ascertained  the  true 


course  between  two  places,  you  must  con- 
struct the  proper  compass  course  by  ap- 
plying the  variation,  and  the  rule,  there- 
fore, is 

To  convert  a  true  course  into  a  compass 
course. — Variation  westerly,  compass  course 
to  the  right  of  true  course ;  variation  east- 
erly, compass  course  to  the  left. 

To  illustrate  for  yourself,  draw  a  large 
circle  and  mark  off  the  compass  points  on 
it.  Now  cut  out  of  stiff  paper  a  miniature 
compass -card  with  the  points  marked. 
Fasten  it  by  a  pin  through  its  centre  to 
the  centre  of  your  large  circle.  By  turn- 
ing the  north  point  of  the  compass  -  card 
as  many  points  to  the  right  or  left  of  the 
fixed  or  true  north  as  you  have  variation 
east  or  west,  you  will  see  at  once  how  each 
separate  point  on  the  compass  is  affected. 


DEVIATION 

In  addition  to  the  magnetism  of  the 
earth,  which  affects  all  compasses  alike,  no 
matter  how  situated,  we  have  to  contend 
with  deviation,  which  is  a  local  error  caused 
by  the  influence  of  neighboring  iron  or 


steel.  In  ships  built  of  either  of  these 
metals  this  influence  is  very  great,  and  no 
compass  aboard  such  a  ship  is  ever  quite 
correct,  except  possibly  on  one  or  two 
courses.  As  the  compass  -  card  does  not 
turn  with  the  ship  when  her  course  is  al- 
tered, it  follows  that  the  mass  of  metal  of 
which  she  is  composed  assumes  new  re- 
lations to  the  needles  of  the  compass,  and 
that,  as  a  result,  the  error  caused  by  devia- 
tion must  change  whenever  the  course  is 
changed. 

This  is  what  makes  the  problems  aris- 
ing from  deviation  extremely  troublesome, 
and  it  makes  it  necessary  to  ascertain  the 
amount  of  error  on  each  course.  It  is  cus- 
tomary in  merchant  vessels  to  use  what 
are  called  compensated  compasses.  Before 
leaving  port  an  expert,  called  a  compass 
adjuster,  ascertains  the  amount  and  direc- 
tion of  the  deviation  of  each  compass  on 
the  principal  courses,  and  endeavors,  by 
placing  magnets  in  the  deck,  to  counter- 
act it.  A  certain  amount  of  error  al- 
ways remains.  This  is  noted  by  the  ad- 
juster, who  will  furnish  the  master  of  the 
ship  with  a  table  of  residual  errors,  show- 
ing the  amount  and  direction  of  the  devi- 


i6 


ation  remaining  on  each  course  after  ad- 
justment. 

Do  not  place  great  faith  in  these  tables, 
for  deviation  changes  in  different  lati- 
tudes, and  the  residual  errors  will  be  al- 
tered. 

It  is  not  possible  to  treat  the  subject  of 
deviation  exhaustively  in  an  elementary 
work  of  this  kind.  The  student  will  be 
shown  how  to  ascertain  his  deviation  on 
each  course  and  to  make  the  necessary 
corrections.  This  is  the  only  trustworthy 
method  of  dealing  with  this  difficulty  of 
navigation,  and  for  the  purposes  of  simple 
practice  it  is  all  that  the  beginner  needs 
to  know. 

But  no  man  is  fit  to  take  entire  charge 
of  the  navigation  of  any  vessel  who  does 
not  know  all  about  the  nature  and  causes 
of  errors  of  the  compass.  Therefore  the 
student  who  aspires  to  mastery  of  the  art 
of  navigating  should  read  Chap.  II.,  Part 
I.,  and  Chap.  XII.,  Part  II.,  of  Lecky's 
Wrinkles  in  Practical  Navigation,  Evans's 
Elementary  Manual  for  Deviation  of  the 
Compass,  and  Towson's  Deviation  of  the 
Compass. 

Some  important  cautions  may  be  given 


here.  Keep  all  iron  and  steel  as  far  from 
your  compasses  as  possible. 

Bear  in  mind  that  magnetic  influence 
will  not  be  stopped  by  placing  anything 
between  the  compass  and  the  iron  or  steel. 
It  will  pass  through  a  stone  wall. 

If  you  use  compensated  compasses,  see 
that  the  magnets,  once  placed  by  the  ad- 
j usters,  are  let  severely  alone.  They  should 
never  be  touched. 

Make  it  an  invariable  rule  to  ascertain 
the  deviation  of  the  compass  on  every 
course  steered  by  the  methods  hereinafter 
explained,  and  to  correct  the  course  ac- 
cordingly. 

Bear  in  mind  when  ascertaining  your 
deviation  that  it  is  good  only  for  that  one 
course.  If  your  ship  is  heading  E.S.E.  and 
you  find  the  deviation  to  be  10°  E.,  it  will 
be  something  else  the  moment  you  alter 
the  course  to  E.-by-S.,  or  even  E.S.E.^E. 

Bear  in  mind  in  taking  bearings  to  ap- 
ply the  deviation  according  to  the  direc- 
tion of  the  ship's  head.  For  instance,  you 
are  lying  at  anchor.  Your  compasses  have 
just  been  adjusted.  The  ship's  head  points 
N.W.-by-N.  The  table  of  errors  says  that 
on  that  course  the  deviation  is  one  point 


i8 


easterly.  Directly  on  your  starboard  beam 
is  a  light-house.  You  wish  to  get  its  bear- 
ing. The  compass  says  it  bears  N.E.-by-E. 
But  you  have  one  point  easterly  devia- 
tion. Hence  the  correct  compass  bearing 
is  E.N.E. 

The  corrections  for  deviation  are  applied 
in  exactly  the  same  way  as  those  for  vari- 
ation. Use  the  same  rules. 

Large  vessels  carry  more  than  one  com- 
pass. One  of  these  is  situated  above  the 
deck  and  as  far  away  from  local  influences 
as  possible.  It  is  called  the  standard  com- 
pass, and  the  ship  is  navigated  by  it. 

To  set  a  course  by  a  standard  compass. — 
Stand  by  the  standard  yourself  and  station 
a  man  at  the  steering  compass.  Order  the 
helm  to  port  or  starboard  till  the  ship  is 
precisely  on  her  course  by  the  standard. 
At  that  instant  blow  a  whistle  (or  give  any 
other  preconcerted  signal),  and  the  man  at 
the  steering  compass  notes  the  direction 
of  the  ship's  head  according  to  it.  The 
course  which  he  gets  is  the  one  to  be  giv- 
en to  the  helmsman. 


HOW  TO   FIND   THE   DEVIATION 

In  port.  —  Take  the  standard  compass 
ashore,  and  set  it  up  in  a  spot  which  is  pre- 
cisely in  line  between  the  regular  station 
of  the  compass  aboard  ship  and  some  dis- 
tant object  visible  from  said  station.  The 
bearing  of  the  distant  object  by  the  stand- 
ard compass  will  now  be  the  correct  com- 
pass (or  magnetic,  as  it  is  usually  called) 
bearing,  unless  you  have  been  stupid 
enough  to  set  up  your  compass  near  iron 
or  steel. 

Now  take  the  compass  back  aboard  ship 
and  set  it  up  in  its  regular  place.  The 
ship  must  now  be  swung  around  so  as  to 
bring  her  head  successively  on  each  of 
the  32  points  of  the  compass.  At  each 
heading  take  the  bearing  of  the  distant 
object  before  selected.  The  differences 
between  the  bearing  obtained  ashore  and 
those  now  obtained  will  be  the  deviations 
for  the  successive  headings  of  the  ship. 
Your  results  should  be  tabulated  thus  : 

Magnetic  bearing           Course  Compass  bearing      Deviation 

S.  42°  W N S.  43°  W i°  W. 

S.  42°  W N.-by-E S.  40°  W 2°  E. 

S.  42°  W N.N.E S.  49°  W 7°  W. 

S.  42°  W N.E.-by-N....S.  38°  W 4°  E. 


And  so  on  to  N.-by-W.  Your  deviations, 
of  course,  will  not  vary  thus  from  east  to 
west.  These  figures  are  used  simply  to 
give  practice  in  the  application  of  the 
rules  for  the  correction  of  deviation  and 
variation.  If  the  compass  bearing  is  to 
the  right  of  the  correct  magnetic  bearing 
the  deviation  is  westerly,  and  if  to  the  left, 
easterly. 

By  the  sun.  —  Some  compasses  are  pro- 
vided with  a  shadow  pin,  which  sets  up  in 
the  centre  of  the  instrument.  The  sun  casts 
a  shadow  of  this  pin,  which  falls  on  the 
card  at  the  bearing  opposite  to  that  of  the 
sun.  Thus,  if  the  shadow  falls  S.S.W., 
the  sun  bears  N.N.E.  You  can  thus  get 
the  compass  bearing  of  the  sun. 

A  better  arrangement  is  the  azimuth  at- 
tachment. This  is  an  arm  with  an  upright 
at  each  extremity.  It  is  arranged  so  that 
these  uprights  are  directly  opposite  one 
another  outside  the  circumference  of  the 
compass.  Each  upright  is  slit  down  the 
centre.  In  one  is  stretched  a  perpendicu- 
lar hair,  while  the  other  is  fitted  with  an 
eye-piece  and  a  colored  shade  to  deaden 
the  rays  of  the  sun.  By  sighting  through 
the  eye-piece  and  the  hair  one  can  get  an 


AZIMUTH   ATTACHMENT 


accurate  bearing 
of  the  sun  or  any 
other  object. 

Having  ob- 
tained the  com- 
pass bearing,  you 
consult  Burd- 
wood's  or  Da- 
vis's  Azimuth 
Tables,  which  give  the  true  bearing  of  the 
sun  for  every  four  minutes  in  the  day. 
Burdwood's  is  for  latitudes  from  60°  to  30°, 
and  Davis's  thence  to  the  equator.  Take 
a  compass  bearing  of  the  sun  and  note  the 
time.  Ascertain  from  Burdwood  or  Davis 
the  true  bearing.  The  difference  between 
this  and  your  compass  bearing  will  be  the 
total  error  of  the  compass,  embracing  both 
variation  and  deviation.  The  chart  gives 
the  variation.  Take  it  from  the  total  error 
and  you  have  the  deviation  left. 

EXAMPLE 

Sun's  true  bearing  at  3. 1 5  P.M N.  150°  W=S.  30°  W. 

Variation  by  chart 10°  W. 

Correct  compass  (magnetic)  bearing S.  40°  W. 

Bearing  by  ship's  compass S.  27°  W. 

Deviation 13°  E. 

You  may  ask  why  it  is  not  sufficient  to 
know  the  total  error  of  the  compass  with- 


out  ascertaining  the  deviation.  The  an- 
swer is  that  you  may  hold  one  course  till 
you  have  changed  your  variation.  If  you 
do  not  know  the  deviation,  you  must  now 
take  another  azimuth. 

Another  method  of  using  the  sun  is  by 
amplitudes,  observed  at  rising  or  setting. 
The  true  bearings  are  given  in  Table  39, 
Bowditch.  In  using  this,  as  well  as  Burd- 
wood  or  Davis,  you  must  know  the  latitude 
of  your  ship  and  the  declination  of  the 
sun,  which  is  obtained  from  the  nautical 
almanac  for  the  day.  The  peculiarity  of 
the  table  of  amplitudes  is  that  it  gives  the 
bearings  as  so  many  degrees  N.  or  S.  of  E. 
and  W.  Thus  with  latitude  15°  N.,  decli- 
nation 6°  N.,  you  get  from  the  table  an 
amplitude  of  6.2,  which  at  sunset  would  be 
read  W.  6°  12'  N.,  the  true  bearing  of  the 
sun. 

Any  other  heavenly  body  whose  declina- 
tion is  not  greater  than  the  range  given  in 
either  the  azimuth  or  amplitude  tables  can 
be  used  exactly  as  the  sun  is.  A  method 
of  finding  the  true  bearing  of  any  celes- 
tial body,  no  matter  how  great  its  declina- 
tion, will  be  given  in  the  proper  place. 


LEEWAY 

Leeway  is,  of  course,  not  an  error  of  the 
compass ;  but  as  it  has  to  be  considered  in 
the  correction  of  compass  courses  in  dead- 
reckoning,  it  is  convenient  to  introduce 
the  subject  here.  A  vessel  sailing  on  a 
wind,  or  even  with  the  wind  abeam,  will 
slide  off  to  leeward  more  or  less.  Conse- 
quently her  actual  course  will  not  be  that 
indicated  by  compass,  even  when  cor- 
rected for  variation  and  deviation. 

To  find  the  leeway.  —  Experienced  sail- 
ors can  estimate  the  leeway  by  the  angle 
between  the  vessel's  wake  and  her  keel. 
A  good  plan,  however,  is  to  heave  the  log, 
then  bring  the  line  to  the  centre  of  the 
compass,  and  its  angle  with  the  vessel's 
course  will  show  the  amount  of  lee- 
way. 

To  correct  for  leeway.  —  Leeway  on  the 
starboard  tack  is  the  same  as  westerly  vari- 
ation. Leeway  on  the  port  tack  is  the  same 
as  easterly  variation.  The  corrections  are 
made  in  the  same  way.  A  glance  at  the 
diagram  will  make  this  clear.  The  vessel 
Heading  N.E.  on  the  starboard  tack  and 


DIAGRAM   OF  LEEWAY 


making  a  quarter-point  of  leeway  is  act- 
ually going  N.E.-JN.  The  vessel  on  the 
port  tack  heading  N.W.  and  making  a 
quarter  -  point  of  leeway  is  really  going 
N.W.^N. 

A  good  point  to  remember  is  this :  lee- 
way on  the  port  tack  and  westerly  varia- 
tion or  deviation  are  opposed  to  one  an- 
other, and  the  same  is  true  of  leeway  on 
the  starboard  tack  and  easterly  error.  For 
example,  you  have  a  quarter-point  wester- 
ly variation,  no  deviation,  and  a  quarter- 
point  leeway  on  the  port  tack  ;  the  leeway 
and  variation  counterbalance  one  another, 
and  the  compass  course  is  the  true  course. 
The  form  given  in  the  following  examples 


for  practice  is  that  used  in  computing  a 
vessel's  dead-reckoning : 


Compass 
course 

Leeway 

Variation 

Deviation 

True  course 

S.W.-by-W. 
E.-by-S. 
N.N.E.XE. 
S-  42°  E. 
S.  33°  W. 

#pt.  Port 
3°  Starb. 
&pt  Star. 
6°  Port 
3°  Starb. 

%pt.  W. 
16°  W. 
i  pt.  E. 

20°  W. 

5°E. 

Kpt.  W. 
10°  E. 

2  ptS.  W. 

25°  E. 

3°W. 

s.w.^w. 

E.JKS. 

N.-by-E.KE. 
S.  31°  E. 
S.  32°  W. 

The  student  should  set  himself  many 
problems  of  this  kind  for  practice,  and 
should  not  attempt  to  go  further  with  this 
subject  until  he  has  mastered  this  one 
matter.  Endless  difficulty  will  otherwise 
be  the  result.  A  good  method  of  study  is 
to  use  the  turning-card  mentioned  under 
the  head  of  variation.  But  you  must  in 
the  end  be  able  to  work  without  it.  For 
instance,  in  the  first  example  proceed  thus  : 
Port  tack  and  westerly  variation  are  op- 
posed ;  that  leaves  a  quarter-point  wester- 
ly, which  added  to  a  quarter-point  wester- 
ly (deviation)  gives  a  half  -  point  westerly 
correction ;  a  half-point  to  the  left  of  S.W.- 
by-W.  is  S.W.^W.  In  the  second  example, 
starboard-tack  leeway  and  westerly  varia- 
tion add,  giving  19°  westerly  correction; 
subtract  10°  and  you  have  9°  westerly  left; 


9°,  or  about  three-quarters  of  a  point,  to  the 
left  of  E.-by-S.  is  E.JS. 


THE  LOG 

There  are  two  kinds  of  logs,  the  chip 
log  and  the  patent  or  taffrail  log.  The 
principal  parts  of  the  chip  log  are  the  chip, 
the  reel,  the  line,  and  the  toggle.  A  sec- 
ond-glass is  used  for  measuring  the  time. 


Reel 


Line 


CHIP    LOG  AND   REKL 


The  chip  is  a  triangular  piece  of  wood, 
rounded  on  its  lower  edge  and  ballasted 
with  lead  to  make  it  ride  point  up.  The 
toggle  is  a  little  wooden  case  into  which  a 
peg,  joining  the  ends  of  the  two  lower 
lines  of  the  bridle,  is  set  in  such  a  way  that 
a  jerk  on  the  line  will  free  it,  causing  the 
log  to  lie  flat  so  that  it  can  be  hauled  in. 
The  inboard  end  of  the  line  is  wound 
around  the  reel.  The  first  10  or  15  fath- 
oms of  line  from  the  log-chip  are  called 
"  stray  line,"  and  the  end  of  this  is  distin- 
guished by  a  mark  of  red  bunting  6  inches 
long.  Its  purpose  is  to  let  the  chip  get 
clear  of  the  swirl  under  a  vessel's  counter 
before  reckoning  begins. 

The  knots,  as  they  are  called,  are  dis- 
tinguished by  running  pieces  of  fish-line 
through  the  strands  to  the  number  of  one, 
two,  three,  etc.  A  piece  of  white  bunting, 
two  inches  long,  marks  every  two-tenths 
of  a  knot.  This  is  because  the  run  of  a 
ship  is  recorded  in  knots  and  tenths. 

A  new  log-line  should  be  soaked  in  wa- 
ter a  few  days  before  marking,  and  always 
before  leaving  port  you  should  soak  your 
line  and  then  see  that  the  marks  are  all  at 
the  proper  distances. 


The  log  -  glass,  in  appearance  like  an 
hour-glass,  measures  28  seconds.  For  high 
rates  of  speed,  a  14-second  glass  is  used, 
and  then  the  number  of  knots  shown  by 
the  line  must  be  doubled.  In  damp  weath- 
er a  watch  is  better  than  a  sand-glass. 

The  principle  of  the  chip  log  is  that  the 
length  of  a  knot  bears  the  same  ratio  to 
the  nautical  mile  (6086  feet)  as  the  time  of 
the  glass  does  to  the  hour.  Hence  we  get 
this  proportion  :  As  the  number  of  seconds 
in  an  hour  is  to  the  number  of  feet  in  a 
mile,  so  is  the  number  of  seconds  in  the 
glass  to  the  number  of  feet  in  the  knot. 

3600  :  6086  :  :  28  sec.  :  x 
x  =  47  feet  4  inches. 

The  speed  of  the  ship  is  recorded  in  the 
log-book  in  knots  and  tenths  of  a  knot. 

How  to  heave  the  chip  log. —  Have  an 
assistant  to  hold  the  glass.  See  that  all 
the  sand  is  in  the  bottom.  Heave  the 
log-chip  well  out  to  leeward  from  the  stern, 
and  hold  the  reel  so  the  line  will  run  free- 
ly. As  soon  as  the  stray  line  is  out  call 
"  Turn,"  and  the  assistant  must  turn  the 
glass  quickly  and  start  the  sand  running. 
The  instant  the  sand  has  passed  down 


the  assistant  must  call  "  Stop,"  and  you 
check  the  line.  Note  the  number  of  knots 
and  tenths  and  haul  in. 

The  chip  log  should  be  hove  every  hour. 
If  the  speed  varies  between  hours  it  must 
be  estimated,  or  the  log  hove  again. 

The  patent  or  towing  log  consists  of  a 
dial,  a  line,  and  a  rotator  of  screw-propel- 


PATENT   OR   TOWING   LOG 


ler  form.  The  action  of  the  water  on  the 
rotator,  which  is  at  the  end  of  the  line  and 
thrown  overboard,  causes  the  line  to  make 


a  certain  number  of  twists  a  minute.  These 
twists  are  proportional  to  the  speed  of  the 
vessel,  and  they  move  the  machinery  of 
the  dial,  which  records  miles  and  fractions 
of  a  mile. 

In  setting  a  taffrail  log  to  work,  you  must 
note  where  the  dial  stands  at  the  time 
when  you  throw  over  the  rotator.  You 
needn't  look  at  it  again  till  you  are  about 
to  change  your  course.  The  difference  be- 
tween the  first  reading  and  the  second  is 
the  distance  run.  Directions  for  the  use 
and  care  of  patent  logs  are  given  by  the 
dealers. 

Both  logs  are  liable  to  error.  The  rota- 
tor of  the  patent  log  slips  sometimes,  and 
that  underrates  the  distance  gone.  Usually, 
however,  they  overrate.  The  chip  log  is 
likely  to  underrate  with  a  following  sea, 
which  causes  the  chip  to  "come  home," 
and  to  overrate  a  little  with  a  head  sea. 

With  both  logs  you  must  allow  for  cur- 
rents. If  sailing  in  a  current  known  to  be 
against  the  ship,  you  must  deduct  its  rate 
from  that  recorded  by  the  log.  If  sailing 
with  the  current,  you  must  add  its  rate. 

Reason :  The  log  measures  your  speed 
through  the  water.  What  you  wish  to  as* 


certain  is  your  actual  movement  over  the 
surface  of  the  globe. 

Example:  Between  Brenton's  Reef 
Light  -  ship  and  Cuttyhunk,  bound  east, 
speed  by  chip  log  was  10  knots,  tidal  cur- 
rent setting  to  the  eastward  i \  knots  per 
hour;  what  did  the  ship  make  per  hour? 
Ans.,  1 i  J  knots. 

Again  :  At  sea  in  the  Gulf  Stream,  head- 
ing S.-by-W.,  patent  log  between  8  A.M. 
and  12  M.  registered  32  miles,  stream  run- 
ning N.-by-E.  2  knots  per  hour ;  what  was 
the  actual  distance  made  ?  Ans.,  24  miles. 

Directions  for  making  allowance  for  cur- 
rents setting  diagonally  across  the  course 
will  be  given  in  the  proper  place.  The  ex- 
istence of  a  known  current,  its  direction 
and  speed,  and  the  length  of  time  the  ship 
is  affected  by  it,  should  be  entered  in  the 
log.  The  necessary  allowance  for  its  effect 
on  the  ship's  run  is  made  by  the  navigator 
when  computing  his  day's  reckoning. 

In  shallow  water,  but  out  of  sight  of  land- 
marks, a  vessel  drifting  in  a  tideway  may 
use  a  ground  log.  This  is  a  common  log- 
line  with  a  hand  lead  attached,  and  it 
shows  the  actual  speed  of  the  ship  over  the 
ground. 


THE  LEAD-LINE 

The  lead  is  used  to  ascertain  the  depth 
of  water,  and,  when  necessary,  the  charac- 
ter of  the  bottom.  There  are  three  kinds 
of  leads :  the  hand  lead,  coasting  lead, 
and  deep-sea  lead.  The  first  weighs  from 
7  to  14  Ibs.,  and  has  markings  to  20  fath- 
oms. The  second  weighs  from  25  to  50 
Ibs.,  and  is  used  up  to  100  fathoms.  The 
third  weighs  from  80  to  1 50  Ibs.,  and  is  used 
in  depths  over  100  fathoms.  The  hand 
lead  is  marked  thus  : 

2  fathoms,  2  strips  of  leather. 


a  white  rag. 

a  red  rag. 

a  piece  of  leather  with  a  hole  in  it. 

same  as  at  3. 


3 

5 

7 
10 
13 
IS 

with  2  knots. 

Large  hand  leads  and  coasting  leads  are 
marked  above  20  fathoms  with  an  addi- 
tional knot  at  every  lo-fathom  point  (30, 
40,  50,  etc.),  and  a  single  knot  at  each  inter- 
vening 5-fathom  point  (25,  35, 45,  etc.). 

The  large  hand  leads,  coast  and  deep- 
sea  leads  are  hollowed  out  on  the  lower 
end  so  that  an  "  arming  "  oi  tallow  can  be 


33 


put  in.  This  will  bring  up  a  specimen  of 
the  bottom,  which  should  be  compared 
with  the  description  found  on  the  chart. 

All  first  -  class  sea  -  going  vessels  should 
discard  the  deep-sea  lead  for  Sir  William 
Thompson's  sounding-machine.  This  ap- 
paratus consists  of  a  cylinder  around  which 
are  wound  about  300  fathoms  of  piano  wire. 
To  the  end  of  this  is  attached  a  heavy 
lead.  An  index  on  the  side  of  the  instru- 
ment records  the  number  of  fathoms  of 
wire  paid  out.  Above  the  lead  is  a  copper 
cylindrical  case  in  which  is  placed  a  glass 
tube  open  only  at  the  bottom  and  chem- 
ically colored  inside.  The  pressure  of  the 
sea  forces  water  up  into  this  tube,  as  it  goes 
down, a  distance  proportionate  to  the  depth, 
and  the  color  is  removed.  When  hoisted, 
the  tube  is  laid  upon  a  prepared  scale,  and 
the  height  to  which  the  water  has  been 
forced  inside  shows  the  depth  in  fathoms 
on  this  scale. 


CHARTS 

A  chart  is  a  map  of  an  ocean,  bay,  sound, 
or  other  navigable  water,  showing  the  con- 
formation of  the  coasts,  heights  of  moun- 
tains, the  depth  at  low-water,  direction  and 
velocity  of  tidal  currents,  location,  charac- 
ter, height  and  radius  of  visibility  of  all 
beacon  lights,  location  of  rocks,  shoals, 
and  buoys,  and  nature  of  the  bottom  wher- 
ever soundings  can  be  obtained. 

The  top  of  the  chart  is  generally  north. 
If  for  any  reason  it  is  otherwise,  north  will 
be  indicated  by  the  north  point  of  a  com- 
pass-card printed  somewhere  on  the  chart. 

On  the  majority  of  small  charts,  such  as 
those  of  bays,  harbors,  and  sounds,  the 
compass  on  the  chart  includes  the  varia- 
tion ;  that  is,  its  north  point  is  slewed  east 
or  west,  just  as  that  of  a  real  compass 
(without  deviation)  would  be  in  that  place. 
In  laying  off  courses  by  such  a  compass 
you  do  not  have  to  allow  for  variation,  be- 
cause it  is  already  allowed  for.  On  large 
charts,  such  as  that  of  the  North  Atlantic, 
the  compass  is  printed  true,  and  the  varia- 
tion is  indicated  by  lines  marked  with  the 
direction  and  amount. 


35 


Parallels  of  latitude  are  shown  by  straight 
lines  across  the  chart.  The  degrees  and 
minutes  are  marked  on  the  perpendicular 
border. 

Meridians  of  longitude  are  shown  by 
straight  lines  up  and  down  the  chart,  and 
the  degrees  and  minutes  are  recorded  on 
the  horizontal  border. 

The  navigator  should  know  the  varieties 
of  buoys.  Channels  on  the  United  States 
coasts  are  indicated  by  red  buoys  with 
even  numbers  situated  on  the  starboard 
side  coming  in  from  the  sea,  and  black 
buoys  with  odd  numbers  on  the  port 
side. 

Buoys  with  black-and-white  perpendicu- 
lar stripes  are  in  mid-channel  and  must  be 
passed  close  to. 

Buoys  with  red  -  and  -  black  horizontal 
stripes  indicate  obstructions  with  channels 
on  both  sides. 

The  abbreviations  on  charts  are  easily 
understood. 

Soundings  on  plain  white  are  in  fathoms ; 
those  on  shaded  parts  are  in  feet.  On  large 
ocean  charts  fathom  curves,  showing  the 
range  of  soundings  of  10,  20,  30,  40,  etc., 
fathoms  are  shown.  They  are  of  great  as- 


sistance  in  taking  soundings  as  you  ap- 
proach a  coast. 

A  light  is  indicated  by  a  red  and  yellow 
spot.  F.  means  fixed  ;  Fl.,  flashing  ;  Int., 
intermittent ;  Rev.,  revolving,  etc. 

An  arrow  indicates  a  current  and  its  di- 
rection. The  speed  is  always  recorded. 

Rocks  just  under  water  are  shown  by  a 
cross  surrounded  by  a  dotted  circle ;  rocks 
above  water,  by  a  dotted  circle  with  dots 
inside  it. 

The  charts  used  by  mariners,  except  in 
great-circle  sailing,  are  called  Mercator's 
charts.  Speaking  roughly,  this  chart  is 
constructed  on  the  imaginary  theory  that 
the  earth  is  cylindrical.  Hence  the  me- 
ridians of  longitude,  which  in  a  sphere  (see 
diagram)  converge  at  the  poles,  are  opened 
out  and  become  straight,  parallel  lines. 
This  compels  a  stretching  out  in  width  of 
everything  represented  in  high  latitudes. 
To  preserve  the  geographical  relations  the 
length  is  also  stretched  proportionately,  so 
that  although  everything  in  high  latitudes  is 
on  too  large  a  scale  as  compared  with  places 
in  lower  latitudes,  the  courses  and  distances 
measured  on  a  chart  are  correct.  The  ad- 
vantage of  a  chart  made  in  this  way  is  that  it 


SPHERE  COMPARED  WITH   MBRCATOR's  CHART 


enables  the  course  of  a  ship  to  be  represent- 
ed by  a  straight  line,  whereas  on  a  sphere  it 
would  be — and  truthfully  so— a  curved  one. 

In  very  high  latitudes  the  inexactness  of 
a  Mercator's  chart  reveals  itself  fully.  It 
is  quite  impracticable  for  polar  navigation. 
For  instance,  how  can  you  steer  for  the 
north  pole  on  a  chart  whose  meridians 
never  come  together  at  any  pole,  but  are 
infinitely  prolonged  parallel  lines?  Owing 
also  to  this  inexactness  the  bearings  of 
distant  objects  are  not  always  quite  correct 
when  laid  down  in  straight  lines  on  the 
chart.  But,  taking  it  all  in  all,  the  Merca- 
tor's chart  is  the  one  best  adapted  to  the 
daily  needs  of  the  mariner. 

By  means  of  the  chart  the  navigator  may 
at  times  sail  along  a  coast  in  clear  weather 
without  having  recourse  to  any  other  in- 
struments of  navigation  than  the  compass 
and  lead-line. 

The  instruments  used  in  consulting  the 
chart  are  the  parallel  rules,  dividers,  and 
course-protractor. 

The  parallel  rules  are  made  of  ebony  or 
gutta-percha.  They  are  connected  by  cross- 
pieces  of  brass,  working  on  pivots  in  such 
a  way  that  the  rules  may  be  spread  apart 


or  pushed  together,  but  will 
always  remain  parallel  to 
each  other. 

They  are  used  to  deter- 
mine the  direction  of  courses. 
For  instance,  you  wish  to  find 
the  course  from  Sandy  Hook 
Light-ship  to  Fire  Island 
Light.  Lay  the  parallel  rules 
so  that  one  edge  cuts  both 
places.  Now  slide  first  one 
rule  and  then  the  other,  hold-  PARALLEL  RULKS 
ing  the  unmoved  one  down 
firmly  so  as  to  retain  the  direction  till  the 
edge  cuts  the  centre  and  circumference 
of  the  compass  printed  on  the  chart.  The 
edge,  if  the  direction  has  been  preserved, 
will  indicate  the  course. 

The  dividers  are  used  to  measure  distance. 
On  small  charts  take  your  distance  from  the 
scale  of  nautical  miles ;  on  large  ones,  from 
the  latitude  scale  at  the  side  of  the  chart.  A 
minute  of  latitude  is  always  a  mile,  because 
parallels  of  latitude  are  equidistant  at  all 
parts.  A  minute  of  longitude  is  a  mile  only 
at  the  equator,  for  the  meridians  are  always 
coming  nearer  and  nearer  together,  till  at 
the  pole  they  join  and  there  is  no  longitude 


at  all.  Yet,  as  every  parallel  of  latitude  runs 
all  the  way  around  the  earth,  it  is  a  circle  and 
contains  360°.  The  distance  from  A  to  B  will 
be  the  same  number  of  degrees,  minutes, 
and  seconds  whether  measured  on  parallel 
A  or  parallel  E,  but  it  will  not  be  the  same 
number  of  miles.  But  the  distances  from  A 
to  C,  from  C  to  D,  and  from  D  to  E  must  be 
the  same  on  any  meridian,  because  the  lines 
A,  C,  D,  and  E  are  parallel.  That  is  why 
distance  is  measured  on  the  latitude  scale. 


MINUTES   VERSUS   MILES 


Long  courses  are  most  conveniently 
shaped  by  the  course-protractor.  Indeed, 
it  is  a  waste  of  time  to  use  anything  else 
on  a  chart  which  shows  the  meridians.  A 
course-protractor  is  simply  a  piece  of  trans- 


parent  horn  or  celluloid,  with  a  compass- 
card  printed  on  it  and  a  string  hanging 
from  the  centre  of  the  card.  Put  the  pro- 
tractor down  so  that  the  meridian  of  the 
compass  is  exactly  over  a  meridian  of  the 
chart,  and  stretch  the  string  along  your 
course.  It  will  cut  the  point  of  the  com- 
pass-card indicating  the  direction.  You 
must,  of  course,  remember  that  this  gives 
a  true  course,  and  make  the  allowance  for 
variatipn. 

You  can  allow  for  the  variation,  how- 
ever, by  making  the  north  point  of  your 
protractor  compass  point  as  far  east  or 
west  of  the  meridian  as  the  variation  is. 


CHART   SAILING 

To  find  the  position  of  the  ship.  —  The 
best  method  is  that  by  cross-bearings.  Se- 
lect two  objects  marked  on  the  chart,  so 
far  apart  that  each  will  bear  close  to  45°  off 
the  ship,  but  in  opposite  directions.  Take 
accurate  bearings  of  each.  Correct  the 
bearings  for  deviation.  Then  with  the 
parallel  rules  carry  the  bearing  of  one  ob- 
ject from  the  compass-card  printed  on  the 


chart  to  the  object  itself,  and  rule  a  pencil 
line.  Do  the  same  with  the  other  object. 
The  intersection  of  the  two  lines  will  be 
the  position  of  the  ship  at  the  time  the 
sights  were  taken. 

Other  good  methods  require  a  knowl- 
edge of  the  use  of  the  sextant,  and  will  be 
introduced  later  in  this  book. 

Having  established  the  position  of  your 
vessel  either  by  cross-bearings  or  by  run- 
ning close  aboard  of  a  light  or  buoy  whose 
position  is  marked  on  the  chart,  you  give 
your  helmsman  the  first  course.  This 
course  has  been  ascer- 

0^}  tained  by  the  parallel 


/vx^\  rules  and  dividers  ac- 

\  cording  to  the  method 

\  already  described. 

\  To  find  the  distance 

\.    between  two  places  on 
***/  the  chart—  If  the  course 
/      is  due  north  or  south, 
measure  the  distance 
and  refer  it  to  the  lati- 
tude scale  on  the  side 
of  the  chart  precisely 
opposite   the  course. 
MAP  OF  CROSS-BEARINGS    The  number  of  min- 


43 


utes  in  the  distance  as  found  there  will  be 
the  number  of  miles. 

If  the  course  is  due  east  or  west,  proceed 
in  the  same  way. 

If  the  course  is  diagonal,  refer  the  dis- 
tance to  that  part  of  the  latitude  scale  op- 
posite the  middle  of  the  course. 

The  proper  method  is  to  take  off  the 
scale  at  the  side  of  the  chart  with  the  di- 
viders a  convenient  unit,  such  as  two  miles 
or  five  miles,  and  find  how  many  times  it 
is  contained  in  the  course. 

On  plane  charts  of  small  expanses,  such 
as  harbors  or  bays,  take  your  unit  of 
measurement  from  the  scale  of  nautical 
miles  to  be  found  on  the  chart. 

To  find  the  latitude  of  a  place  on  the 
chart. — Measure  the  distance  of  the  place 
from  the  nearest  parallel.  Take  the  di- 
viders to  the  graduated  border  at  the  side 
of  the  chart,  and  put  one  leg  in  the  same 
parallel.  The  other  should  be  in  the  grad- 
uated border  at  the  latitude  required. 

To  find  the  longitude  of  a  place  on  the 
chart.  —  Proceed  in  precisely  the  same 
manner,  but  use  a  meridian  and  the  longi- 
tude border  at  the  top  or  bottom  of  the 
chart. 


To  mark  the  ship's  place  on  the  chart. — 
This  is  to  be  done  at  sea  after  finding  the 
latitude  and  longitude.  "  With  the  di- 
viders take  from  the  graduated  meridian 
the  given  latitude ;  mark  this  on  the  me- 
ridian nearest  the  given  longitude ;  lay  the 
edge  of  a  pair  of  parallel  rulers  on  a  near 
parallel,  and  work  one  side  of  them  to  the 
exact  latitude  you  have  marked  on  the 
meridian  ;  then  with  the  dividers  take  the 
given  longitude  from  the  graduated  paral- 
lel [at  the  top  or  bottom  of  the  chart] ;  lay 
this  down  along  the  edge  of  the  parallel 
rulers  which  already  mark  the  latitude,  and 
you  have  the  ship's  place  "  (Qualtrough). 

To  berth  your  ship  at  an  anchorage. — Se- 
lect the  spot  on  the  chart  where  you  wish 
to  anchor.  Note  the  soundings  at  mean 
low-water  and  have  your  cable  ranges  over- 
hauled for  at  least  three  times  that  depth. 
Draw  a  circle  around  the  spot,  with  a  radius 
about  three  times  the  length  of  the  cable 
to  be  let  go.  See  if  you  will  have  swing- 
ing room  at  all  points  on  the  circumference 
of  the  circle,  and  also  plenty  of  room  for 
getting  under  way  with  the  wind  in  any 
direction,  for  you  may  not  be  able  to 
bring  up  just  at  the  centre  of  your  circle. 


Now  lay  down  cross-bearings  on  the  cir- 
cumference of  your  anchorage  at  the  side 
from  which  you  expect  to  approach  it. 
When  you  get  those  bearings  on  your  com- 
pass, round  up  and  let  go.  After  anchor- 
ing ascertain  the  exact  position  of  your 
vessel  by  new  cross-bearings,  and  note  the 
same  in  the  log. 

In  setting  a  course  on  a  chart,  carefully 
note  the  direction  and  speed  of  the  tidal 
currents.  Refer  to  your  tide  tables  and 
find  out  just  where  the  tide  is  and  make 
allowance  accordingly.  Remember  that 
the  tide  ebbs  6  hours  and  flows  6  hours, 
but  in  many  places  the  currents  do  not 
change  for  some  time  after  the  hours  of 
high  and  low  water.  These  points  you 
can  learn  only  from  local  watermen,  or 
from  the  pages  of  the  Atlantic  Coast  Pilot 
and  similar  works. 

To  find  the  ship's  position  when  sailing 
along  the  land. — Take  a  compass  bearing 
of  a  light  or  other  prominent  object  when 
it  is  2,  3,  or  4  points  off  the  course.  Take 
another  bearing  when  it  has  doubled  the 
first  and  is  4,  6,  or  8  points  off  the  course. 
The  distance  run  by  the  ship  between  the 
two  bearings  will  be  her  distance  from 


the  observed  object 
at  the  second  bear- 
ing. 

In  the  diagram  the 
ship  at  A  heading 
north  finds  the  light 
bearing  N.N.W., 
2  points  off  her 
course.  At  B  she 
finds  it  bears  N.W., 
4  points  off.  The  log 
makes  the  distance 
from  A  to  B  7  miles. 
This  will  be  almost 
the  exact  distance  of 
the  light  from  the 
ship  at  B.  The  com- 
monest form  of  this 

problem  is  that  used  at  positions  B  and  C, 
with  the  object  4  points  off  the  course  and 
exactly  abeam.  This  is  known  as  the  bow- 
and-beam  bearing.  The  navigator  will  find 
cases  in  which  the  other  form  is  conven- 
ient. This  method  should  be  practised 
continually,  as  it  is  the  standard  method  in 
coastwise  navigation.  It  is  also  valuable  in 
establishing  a  final  position  with  reference 
to  the  land  when  about  to  go  to  sea. 


COASTWISE   BEARINGS 


47 


How  to  use  compass,  log,  and  lead  in  a  fog. 
—Take  a  piece  of  tracing-paper  and  rule  a 
meridian  on  it.  Take  casts  of  the  lead  at 
regular  intervals,  noting  the  time  at  which 
each  cast  is  taken,  and  the  distance  logged 
between  each  two.  The  compass  shows 
the  course.  Now  rule  a  line  on  the  trac- 
ing-paper in  the  direction  of  your  course. 
Measure  off  on  it  by  the  scale  of  miles  of 
your  chart  the  distances  run  between  casts. 
Opposite  .each  cast  note  the  time  and  the 
depth  ascertained.  It  is  a  good  thing  to 
add  also  the  char- 
acter of  the  bottom. 
Now  lay  your  trac- 
ing-paper down  on 
the  chart,  which  can 
be  seen  through  it, 
in  the  neighborhood 
of  the  position  you 
believed  yourself  to 
be  in  when  you 
made  the  first  cast. 
If  your  chain  of 
soundings  agrees 
with  those  on  the 
chart  right  under  12  /  9  **. 

your    Course,    all    is  CHAIN  OF  SOUNDINGS 


right.  If  not,  move  the  tracing  -  paper 
about,  keeping  the  meridian  line  due  north 
and  south,  till  you  find  the  place  on  the 
chart  that  does  agree  with  you.  That 
is  where  you  are.  You  will  not  find  two 
places  where  you  can  get  that  chain  of 
soundings  on  the  same  course  and  at  the 
same  distances. 

This  is  the  only  method  by  which  a 
ship's  position  can  be  found  with  any  cer- 
tainty on  soundings  in  thick  weather. 
There  is  no  excuse  whatever  for  the  man 
who  runs  his  vessel  ashore,  if  he  has  not 
tried  this. 


DEAD   RECKONING 

To  ascertain  the  position  of  a  ship  at 
sea  by  keeping  account  of  the  courses  and 
distances  which  she  sails,  we  proceed  on 
the  theory  that  small  sections  of  the  sur- 
face of  the  earth  are  flat.  The  whole  mat- 
ter then  resolves  itself  into  the  solution  of 
right  -  angled  triangles.  A  single  glance 
will  show  the  student  that  any  of  the 
courses  ruled  on  the  diagram  chart  unite 
with  the  parallels  and  meridians  in  forming 


8o°  70°  60°  50°  40° 


40® 


20° 


DIAGRAM   CHART 


series  of  right-angled  triangles.  The  only 
cases  in  which  no  such  triangles  exist  are 
those  of  sailing  due  east  and  west  or  due 
north  and  south. 

The  problems  to  be  solved  in  sailing  on 
the  open  sea  out  of  sight  of  land  are  these  : 
Having  left  a  known  point  and  sailed  so 
many  miles  in  such  and  such  direction, 
what  latitude  and  longitude  have  we  ar- 
rived at,  and  what  are  the  course  and  dis- 


5° 


tance  thence  to  our  point  of  destina- 
tion ? 

If  you  are  sailing  due  north  or  south,  the 
problem  is  extremely  simple.  Suppose  your 
position  at  noon  to-day  is  lat.  41°  15'  N., 
long.  40°  W.,  and  up  to  noon  to-morrow  you 
sail  280  miles  north  (true).  It  is  obvious 
that  the  longitude  will  remain  unchanged. 
The  latitude  will  be  280  minutes,  or  4°  40', 
farther  north.  That  4°  40'  is  called  the  dif- 
ference of  latitude,  and  in  this  case  it  is  ob- 
viously to  be  added  to  to-day's  latitude, 
because  we  have  been  increasing  our  lati- 
tude. The  ship's  position  at  to-morrow 
noon,  then,  is  lat.  45°  55'  N.,  long.  40°  W. 

Hence  we  learn  that  the  distance  by 
which  a  ship  changes  her  latitude  north 
or  south  is  called  difference  of  latitude. 

In  sailing  due  east  or  west,  however,  the 
matter  is  not  so  simple,  because  only  on 
the  equator  are  a  nautical  mile  and  a  min- 
ute of  longitude  the  same  thing.  But  if 
we  have  a  table  giving  us  the  number  of 
miles  in  a  degree  of  longitude  at  every  dis- 
tance north  or  south  of  the  equator  (which 
means  in  every  latitude),  we  can  easily  find 
the  longitude.  For  instance,  a  ship  in  lat. 
42°  N.  sails  true  east  100  miles ;  how  much 


does  she  alter  her  longitude?  A  degree 
of  longitude  in  lat.  40°  measures  44.59 
miles.  She  changes  her  longitude  by  2° 
10.8'  or  2°  10'  48" — a  tenth  of  a  minute 
being  6". 

The  number  of  miles,  then,  which  a  ship 
makes  east  or  west  is  called  departure,  and 
it  must  be  converted  into  degrees,  minutes, 
and  seconds  in  order  to  find  the  difference 
of  longitude. 

But  nine  times  out  of  ten  a  ship  sails  a 
diagonal  course.  Suppose  a  vessel  in  lat. 
40°  20'  N.,  long.  60°  15'  W.,  sails  53 
miles  S.W.-by-W.£W.  How  are  .X"  we 
to  find  her  new  latitude  ./^  and 
longitude?  She  has^^  sailed  a 
course  like  this:  x^  Suppose  we 
draw  a  perpendicular  line  to  represent  a 
meridian,  and  a  horizontal  one  to  repre- 
sent a  parallel.  Then  we  shall  have  the 
triangle  ABC,  in  which  the  line  AC  rep- 
resents the  distance  and  direction,  while 
the  angle  at  A  is  the 
angle  of  the  course 
with  the  meridian.  If 
now  we  can  ascertain 
the  length  of  AB,  or 
the  distance  by  which 


she  has  gone  to  the  south,  we  shall  have 
the  difference  of  latitude ;  and  if  we  can 
get  the  length  of  the  line  BC,  we  shall 
have  the  departure  and  from  it  the  differ- 
ence of  longitude.  From  these  two  factors 
we  get  the  new  latitude  and  longitude. 

This  is  a  simple  problem  in  trigonome- 
try, but  no  navigator  need  know  trigonom- 
etry, because  Tables  I.  and  II.  of  Bowditch 
solve  all  possible  problems  of  this  kind  for 
him,  and  he  needs  only  arithmetic. 

The  complete  Navigation  Tables  can  be 
purchased  separate  from  the  rest  of  the 
work,  under  the  title  Useful  Tables,  for 
$1.25. 

Table  I.  is  marked  at  the  top  with  the 
different  courses  from  \  point  up  to  4 
points.  In  three  adjoining  columns  are 
found  distance,  difference  of  latitude,  and 
departure,  marked  Dist.,  Lat.,  and  Dep.  If 
you  are  sailing  on  any  particular  course, 
say  N.N.E.,  you  go  to  the  table  for  2-point 
courses,  look  in  the  distance  column  for 
the  distance  you  have  made  by  your  log, 
and  opposite  to  that  distance  you  will  find 
your  diff.  lat.  and  dep. 

At  4  points  diff.  of  lat.  and  dep.  become 
equal,  because  the  course  is  precisely  half 


Pep.  4.5mffo3 


way  between  no  points  and  8  points.  On 
any  course  less  than  4  points  diff.  lat.  is 
greater  than  dep.,  because  you 
go  more  north  or  south  than  east 
or  west.  On  any  course  greater 
than  4  points  dep.  is  greater 
than  diff.  lat.,  because  you  go 
more  east  or  west  than  north  or 
south.  And  the  relations  of 
the  two  elements  are  simply  re- 
versed, as  may  be  seen 
by  the  diagrams.  In 
a  2- point  course,  the 
diff.  lat.  is  the  same 
as  the  dep.  in  a  6- 
point  course,  the 
complement  of  a  2-point  course.  Hence, 
in  using  the  tables,  as  soon  as  you  have  a 
course  over  4  points,  you  begin  at  the  last 
page  of  the  tables  and  read  up  from  the  bot- 
tom, noting  that  while  dist.  remains  in  the 
same  place,  lat.  and  dep.  are  reversed. 

Suppose  you  have  sailed  28  miles  N.-by- 
W.JW.  Opposite  28  in  the  dist.  column 
under  ij-point  courses  you  find  diff.  lat. 
27.2  miles  and  dep.  6.8  miles. 

Suppose  you  have  sailed  40  miles  E.-by- 
N,  Under  /-point  courses  you  find  (read- 


54 


ing  from  the  bottom  up)  opposite  dist.  40, 
diff.  lat.  7.8,  dep.  39.2. 

Table  II.,  Bowditch,  contains  the  same 
elements  worked  for  courses  in  degrees. 
You  should  now  be  prepared  to  work  such 
examples  as  these : 

A  ship  leaving  lat.  36°  15'  N.,  long.  47°  48' 
W.,  sails  S.E.-by-E.  78  miles.  Required 
the  diff.  lat.,  the  dep.,  and  the  new  lat. 

Ans.  Diff.  lat.  43.3,  dep.  64.9,  new  lat.  35° 
31'  42"  N. 

(Bear  in  mind  that  a  tenth  of  an  hour  or 
a  degree  is  6  minutes ;  a  tenth  of  a  min- 
tue,  6  seconds.) 

A  ship  leaving  lat.  28°  15'  S.,  long.  43°  18' 
E.,  sails  49  miles  N.W.  What  are  the  diff. 
lat.,  dep.,  and  new  lat.  ? 

Ans.  Diff.  lat.  34.6  miles,  dep.  34.6,  new 
lat.  27°  40'  24"  S. 

A  ship  leaving  lat.  i  °  io'N.,  long.  i6°5' W., 
sails  S.S.E.  168  miles.  Give  same  elements. 

Ans.  Diff.  lat.  155.2  miles,  dep. 64.3  miles, 
new  lat.  i°  25'  12"  S. 

A  ship  leaving  lat.  15°  15'  N.,  long.  121° 
31'  E.,  sails  N.  63°  E.  64  miles.  Give  same 
elements. 

Ans.  Diff.  lat.  29.1,  dep.  57,  new  lat.  15° 
44'  6"  N. 


55 


The  full  rule  for  finding  the  new  lat.  is 
as  follows : 

When  the  old  lat.,  known  as  lat.  left,  and 
diff.  lat.  are  both  N.  or  both  S.,  add  them  ; 
when  one  is  N.  and  the  other  S.,  subtract 
the  less  from  the  greater,  and  the  remain- 
der, named  N.  or  S.  after  the  greater,  will 
be  the  new  lat.,  known  as  lat.  in. 

The  next  step  is  to  find  the  diff.  long., 
and  from  it  the  new,  or  long.  in.  The  pro- 
portions of  right-angled  triangles  are  such 
that  all  you  have  to  do  is  to  obey  the  fol- 
lowing rule : 

Find  the  mid.  lat.  between  that  of  yes- 
terday and  that  of  to-day.  Go  to  the  page 
in  Table  II.,  marked  with  the  number  of 
degrees  of  this  mid.  lat.  which  you  have 
just  found,  and  seek  in  the  diff.  lat.  column 
for  the  amount  of  your  dep.  Opposite  to  it  in 
the  dist.  column  will  be  the  figures  indicat- 
ing the  number  of  minutes  in  the  diff.  long. 

Example :  A  ship  in  lat.  36°  15'  N.,  long. 
52°  1 8'  W.,  sails  N.E.-by-N.  60  miles;  re- 
quired the  lat.  and  long.  in. 

Table  I.,  under  the  head  of  3 -point 
courses,  gives  for  60  miles  diff.  lat.  49.9 
miles,  dep.  33.3.  The  lat.  in  is,  therefore, 
37°  4'  54"  N.  To  find  the  mid.  lat.  add 


the  lat.  left  and  the  lat.  in,  and  divide  by  2. 
Take  the  nearest  degree  as  your  answer. 
In  this  case  the  mid.  lat.  is  36°  39'  57",  and 
as  that  is  nearer  37°  than  36°  we  take  the 
former.  Now  turn  to  the  page  for  37°  in 
Table  II.  Apply  the  dep.  33.3  in  the  lat. 
column ;  the  nearest  you  can  come  to  it  is 
33.5,  opposite  which  in  the  dist.  column  is 
42,  which  means  that  in  lat.  37°  a  dep.  of 
33.5  miles  will  equal  42'  diff.  long.  Long, 
left  was  52°  1 8'  W.  We  have  made  42'  diff. 
long,  to  the  eastward,  thus  diminishing  our 
westerly  longitude.  We  subtract  42'  from 
52°  1 8'  W.,  and  get  51°  36' W.  as  our  long.  in. 

This  process  of  working  out  the  latitude 
and  longitude  is  called  middle  latitude  sail- 
ing, and  by  it  the  ordinary  problems  of 
dead  -  reckoning  are  solved.  The  cases 
which  present  themselves  in  the  actual 
practice  of  navigation  are  three  in  number. 

Case  /. — Course  and  distance  sailed  be- 
ing given,  to  find  the  diff.  lat.  and  dep. 

Case  II. — The  lat.  and  long,  left  and  the 
course  and  distance  being  given,  to  find 
the  lat.  and  long.  in. 

Case  III.  —  The  latitudes  and  longitudes 
of  two  places  being  given,  to  find  the 
course  and  distance  between  them, 


Cases  I.  and  II.  have  been  explained,  ex- 
cept as  to  sailing  true  east  or  west,  which 
is  called  parallel  sailing.  Here  there  is  no 
diff.  lat.,  and  the  lat.  in  is  the  mid.  lat.  To 
find  the  diff.  long,  apply  the  distance  sailed, 
which  in  this  case  is  also  the  departure,  in 
the  lat.  column,  and  opposite  it  in  the 
dist.  column  will  stand  the  number  of  min- 
utes in  the  diff.  long. 

To  solve  case  III. — Subtract  the  less  lat- 
itude from  the  greater,  and  reduce  the  re- 
mainder to  minutes.  Do  the  same  with 
the  two  longitudes.  Find  the  mid.  lat.  Go 
to  the  page  in  Table  II.  marked  with  the 
number  of  degrees  in  the  mid.  lat.,  and 
seek  the  diff.  long,  in  the  dist.  column. 
Opposite  to  it  in  the  lat.  column  will  be  the 
dep.  Now  seek  in  Table  II.  for  the  page 
where  the  diff.  lat.  and  the  dep.  stand  be- 
side one  another  in  their  respective  col- 
umns. The  required  dist.  will  stand  op- 
posite in  the  dist.  column,  and  the  course 
either  at  the  top  or  bottom  of  the  page, 
according  as  diff.  lat.  or  dep.  is  the  greater. 

In  using  Tables  I.  and  II.,  if  the  dist.,  lat., 
or  dep.  in  your  problem  happens  to  be  larger 
than  those  contained  in  the  table,  you  can 
obviate  the  difficulty  by  dividing  all  your 


elements  by  10,  because  the  relations  of  all 
the  parts  of  a  right-angled  triangle  one- 
tenth  the  size  of  yours  will  be  just  the  same 
if  you  reduce  all  three  sides  to  one-tenth. 
For  instance,  you  have  diff.  lat.  304' ;  dep. 
2694  miles.  Divide  both  by  10  and  you  have 
30.4  and  269.4,  both  of  which  are  in  the 
tables.  With  those  you  can  find  one-tenth 
of  your  distance,  which  take  out  and  multi- 
ply by  10.  The  angles  all  remain  the  same, 
so  the  course  is  all  right  as  it  stands. 

Example :  A  ship  in  lat.  42°  3'  N.,  long. 
70°  4'  W.,  is  bound  for  St.  Mary's,  lat.  36° 
59'  N.,  long.  25°  10'  W.  What  are  the 
course  and  distance  ? 

Lat.  left 42°  03'  N.     Long,  left ...  .70°  04'  W. 

Lat.  sought 36°  59'  N.     Long,  sought. 2 5°  10'  W. 

Diff.  lat 5°  04'          Diff.  long 44°  54' 

Reduced  to  minutes  =  304  Reduced  to  minutes  =  2604 
Middle  lat 39°  31'. 

As  the  tables  do  not  run  beyond  300  miles, 
we  take  one-tenth  of  2694  (the  diff.  long.), 
269,  and  under  40°  with  this  number  in  the 
dist.  column  we  get  206.1  dep.  out  of  the  lat. 
column.  Now  we  look  for  a  place  where  the 
diff.  lat.  is  30.4  and  the  dep.  206.  i .  As  we  are 
working  with  one-tenth  of  the  dep.,  we  must 
do  the  same  with  304,  the  diff.  lat.,  or,  in  oth- 
er words,  put  a  decimal  mark  before  the  4, 


making  it  30.4.  We  find  under  the  head  of  7^ 
points  diff.  lat.  30.7,  dep.  206.7,  and  opposite 
them  the  dist.  209.  This  is  one-tenth  of  the 
real  distance,  2090  miles.  As  the  diff.  lat. 
was  southward  and  the  diff.  long,  eastward, 
the  course  must  be  S.  7J  points  E.,  or  E.fS. 

EXAMPLES   FOR   PRACTICE 

(From  Norie's  Epitome] 

Required  the  course  and  distance  from 
the  Cape  of  Good  Hope,  lat.  34°  22'  S.,  long. 
1 8°  24'  E.,  to  St.  Helena,  lat.  1 5°  55'  S.,  long. 

5°  45'  W. 

Ans.  Course  N.  50°  W.,  dist.  1717  miles. 

Required  course  and  distance  from  Per- 
nambuco,  lat.  8°  4'  S.,  long.  34°  53'  W.,  to 
Cape  Verde,  lat.  14°  45'  N.,  long.  17°  32'  W. 

Ans.  Course  N.  37°  E.,  dist.  1720  miles. 

A  ship  from  lat.  2°  5'  N.  and  long.  22° 
30'  W.  sails  W.S.W.  256  leagues  (a  league^ 
3  miles).  Required  her  present  lat.  and 
long.,  and  her  course  and  dist.  to  St.  Ann's 
Island,  lat.  2°  15'  S.,  long.  43°  3&'  W. 

Ans.  Lat.  2°  49'  S.,  long.  34°  20'  W.,  course 
N.  86°  W.  dist.  559.6  miles. 

Excellent  practice  may  be  had  by  laying 
off  courses  and  distances  on  charts,  and  then 


6o 


working  out  the  same  by  computation  to 
see  how  near  your  two  results  will  agree. 

WORKING   A  TRAVERSE 

If  a  ship  sailed  for  24  hours  on  one 
course,  the  student  would  now  be  ready  to 
work  out  her  latitude  and  longitude  by 
dead-reckoning.  But  vessels  usually  change 
the  course  several  times  in  the  course  of 
a  day's  run,  and  as  the  reckoning  is  only 
computed  once  a  day  —  at  noon  —  it  be- 
comes necessary  to  have  a  method  of  ob- 
taining the  result  of  several  courses.  This 
is  called  working  a  traverse,  and  it  is  the 
culmination  of  dead-reckoning. 

Suppose  a  vessel  to  start  from  Sandy 
Hook  Lightship,  lat.  40°  28'  N.,  long.  73°  50' 
W.,  and  sail  in  24  hours  S.E.  7  miles,  E.-by- 
S.  6£  miles,  S.W.  9  miles,  and  S.E.-by-S. 
4.35  miles ;  where  would  she  be  at  noon  on 
the  second  day?  The  diagram  shows  us 
that  she  would  be  1 7.7  miles  about  S.S  E/JE. 
of  the  lightship.  The  method  of  calculat- 
ing such  a  compound  course  is  called  work- 
ing a  traverse,  and  is  as  follows  : 

Write  out  the  various  courses  with  their 
corrections  for  variation,  leeway,  and  devi- 
ation, and  the  distance  run  on  each.  In 


TRAVERSE  COURSE  FROM    SANDY   HOOK    LIGHTSHIP 


four  columns,  headed  respectively  N.,  S.,  E., 
W.,  put  down  the  diff.  of  lat.  and  dep.  for 
each  course.  Add  together  all  the  north- 
ings, all  the  southings,  all  the  eastings,  all 
the  westings.  Subtract  to  find  the  differ- 
ence between  northings  and  southings,  and 
you  will  get  the  whole  diff.  lat.  The  dif- 
ference between  eastings  and  westings  will 
give  the  whole  dep. 

With  the  whole  diff.  lat.  and  whole  dep., 
seek  in  Table  II.  for  the  page  where  the  near- 
est agreement  of  lat.  and  dep.  with  your  fig- 
ures can  be  found.  The  number  of  degrees 
at  the  top  or  bottom  of  the  page  (according 
as  diff.  lat.  or  dep.  is  greater)  will  give  you 
the  course  made  good  and  distance. 

Find  the  lat.  in,  as  already  explained. 

Find  the  long,  in,  as  already  explained. 

Example :  A  ship  in  lat.  31°  15'  N.,  long. 
68°  30'  15''  W.,  sails  by  compass  36  miles 
E.-by-S.,  with  i  pt.  W.  van,  £-pt.  E.  dev., 
^-pt.  port-tack  leeway ;  22  miles  S.S.E.  with 
same  variation,  ^-pt.  E.  dev.,  J-pt.  starboard- 
tack  leeway ;  28  miles  S.  by  E.  with  same 
variation,  \  W.  dev.,  £-pt.  port-tack  leeway  ; 
and  31  miles  S.  with  f-pt.  W.  var.,  $-pt.  E. 
dev.,  and  J-pt.  port -tack  leeway.  Re- 
quired the  course  and  distance  made  good 
and  the  new  lat.  and  long. 


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64 


In  this  example  there  is  no  subtraction 
of  southing  and  northing,  or  of  easting  and 
westing.  Let  us  suppose  a  case,  however, 
of  a  ship  beating  to  the  eastward,  and  forced 
to  run  off  to  the  northwest  by  some  acci- 
dent. Omitting  the  corrections  of  the 
compass  course  for  the  sake  of  brevity,  we 
should  have  a  traverse  like  this : 


Lat.  left,  26°  30'  N.                       Long,  left,  48°  25'  W. 

Course 

Distance 

N. 

S.       i      E. 

W. 

S.S.E. 
N.E.XB. 
S.E.^E. 
W.N.W. 

12 

16 
H 
13 

10.7 
5-0 

ii.  I           4.6 
11.9 

8.9        10.8 

12.0 

'5  7 

20.0       |    27.3 
15.7       ,    12.0 

12.0 

4-3            IS-3 

Course  S.  74°  E.     Distance,  16  miles. 


Lat.  left 26°  30'  oo"  N. 

Diff.  lat. . .  4'  * 8"  S. 


Long,  left 48°  25'  W. 

Diff.  long 17'  E. 


Lat.  in 26°  25'  42"  N.  Long,  in 48°  08'  W. 

Currents. — In  case  the  ship  encounters  a 
known  current  setting  diagonally  across 
the  course,  multiply  the  rate  of  the  flow  by 
the  number  of  hours  and  enter  it  as  dis- 
tance, and  enter  the  direction  as  a  course. 

Example:  A  ship  from  lat.  36°  15'  S., 
long.  101°  14'  E.,  sails  in  24  hours  30  miles 
N.N.W.  true,  and  68  miles  W.£N.  true. 


During  12  hours  of  the  day  she  is  in  a 
current  setting  E.^S.  at  the  rate  of  2  knots 
per  hour.  Required  her  course  and  dis- 
tance made  good. 


Course 

Distance 

N. 

S. 

E. 

W. 

N.N.W. 
W.#N. 
E.#& 

30 
68 
24 

27.7 
6-7 

2-4 

23-9 

ii-S 
67.7 

34-4 

2-4 

79.2 
23-9 

32.0 

55-3 

Ans.  Course  made  good,  N.  60°  W.,  dist. 
64  miles. 


HOVE  TO 

A  vessel  hove  to  in  a  gale  comes  up 
towards  the  wind  and  then  falls  off,  and 
her  course  is  a  zigzag.  To  keep  her  reck- 
oning note  how  she  heads  when  she  has 
come  up  as  far  as  she  will,  and  again  when 
she  has  fallen  off  to  the  limit.  The  point 
half  way  between  is  to  be  called  the 
course.  For  instance,  she  comes  up  to  east 
and  falls  off  to  northeast.  The  course  is 
east- northeast. 

The  leeway,  variation,  and  deviation  are 
applied  to  the  course  thus  ascertained. 


66 


Different  ships  make  different  leeway,  and 
the  navigator  must  determine  its  extent  by 
careful  observation. 

Every  time  she  begins  to  come  up  she 
will  go  ahead  a  little.  The  speed  of  this 
progress  or  "  drift "  is  entered  as  the  rate 
in  knots.  The  rest  of  the  operation  is  the 
same  as  in  working  a  traverse. 

Example:  A  vessel  in  lat.  33°  14'  S., 
long.  60°  47'  E.,  is  hove  to  on  the  starboard 
tack.  She  comes  up  to  E.-by-S.,  and  falls 
off  to  E.-by-N. ;  leeway,  6  points ;  drift,  2 
knots  per  hour ;  variation,  22°  E. ;  vessel 
hove  to  24  hours.  What  is  her  position  at 
noon  of  the  second  day  ?  (See  table  on 
page  67.) 


SHAPING  THE  COURSE 

Having  ascertained  the  position  of  the 
ship,  it  becomes  necessary  to  ascertain  the 
course  required  to  sail  to  reach  the  port 
of  destination.  This  may  be  done  by 
using  the  chart,  if  the  distance  is  small  and 
the  scale  of  the  chart  large.  If  the  dis- 
tance is  considerable  and  the  scale  of  the 
chart  small,  much  inaccuracy  will  follow. 


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68 


The  course  is,  therefore,  to  be  found  either 
by  mid.  lat.  or  Mercator's  sailing. 

The  course  is  found  by  mid.  lat.,  accord- 
ing to  the  rule  laid  down  in  Case  III.  of 
dead-reckoning. 

If  the  course  is  more  than  4  points,  mid. 
lat.  will  give  a  satisfactory  result.  But 
if  the  course  is  4  points  or  less,  owing  to 
the  construction  of  Mercator's  charts  with 
their  expansion  of  the  degrees  to  the  north 
or  south,  error  will  creep  in.  Consequent- 
ly Mercator's  sailing  must  be  employed. 
Mid.  lat.  is  good  for  shaping  any  course  if 
it  is  short,  except  in  high  latitudes,  where 
the  Mercator  method  should  always  be 
used. 

To  solve  problems  in  Mercator's  sailing 
the  navigator  must  use  Table  III.  This 
table  contains  the  meridional  parts  corre- 
sponding to  the  increases  in  the  charted 
lengths  of  the  degrees  of  latitude.  These 
parts  are  picked  out  by  finding  the  degrees 
at  the  top  or  bottom  of  the  table,  and  the 
minutes  at  the  side.  Thus  the  meridional 
parts  corresponding  to  19°  45'  are  1201.4; 
9°  36',  574-9  ;  29',  28.8. 

To  shape  the  course  and  find  the  distance 
by  Mercator  s  sailing.— Find  the  difference 


between  the  meridional  parts  correspond- 
ing to  the  lat.  in  and  lat.  sought.  Call 
this  meridional  diff.  lat.  With  the  merid- 
ional diff.  lat.  and  the  diff.  long,  find  the 
course  by  searching  in  Table  II.  for  the 
page  where  they  stand  opposite  one  anoth- 
er in  the  lat.  and  dep.  columns.  Under 
this  course  find  the  distance  opposite  the 
proper  (not  meridional)  diff.  lat. 

Example :  What  are  the  course  and  dis- 
tance from  Sandy  Hook  Lightship,  lat.  40° 
28'  N.,long.  73°  50' W.,  to  lat.  39°  51'  N., 
long.  72°  45'  W.  ? 

Lat.  in 40°  28'  Mer.  parts 2644.5 

Lat.  sought .39°  51'  Mer.  parts .2596.2 

Proper  diff.  lat o°  37'  Mer.  diff.  lat 48.3 

Long,  in 73°  50'  W. 

Long,  sought .72°  45'  W. 

Diff.  long i°  05'=  65' 

On  the  page  in  Table  II.  which  has  37° 
at  the  top  and  53°  at  the  bottom  we  find 
64.7  and  48.7  opposite  one  another.  This 
is  the  nearest  agreement  to  the  meridional 
diff.  lat.  and  the  diff.  long,  that  we  can  find. 
As  the  48.7  is  in  the  right-hand  column 
we  must  read  the  table  up  from  the  bot- 
tom, and  this  gives  us  a  course  of  53°. 
Our  course  is,  therefore,  S.  53°  E.  Under 


53°,  applying  our  proper  diff.  lat.,  37',  in 
the  lat.  column  we  find  37.3,  opposite  which 
is  our  distance,  62  miles. 


NAVIGATION   BY  OBSERVATION 

Navigation  by  observation  is  carried  on 
by  measuring  the  altitude  of  the  sun,  the 
moon,  or  a  star,  and  computing  from  this 
and  certain  other  data  the  latitude  or  lon- 
gitude of  the  ship.  The  altitude  of  a  celes- 
tial body  is  expressed  in  terms  of  degrees 
and  minutes/and  is  that  part  of  90°  con- 
tained between  the  body  and  the  sea  hori- 
zon. 

An  observer  standing  at  the  point  G  in 
the  diagram  would  see  the  horizon  at  E 


90° 


i 


and  F,  and  the  apparent  sky  stretching  from 
one  side  to  the  other  in  a  semicircle,  or 
rather  hemisphere.  Now  a  circumference 
of  this  semicircle  is  divided,  like  any  other, 
into  1 80°.  Supposing  the  sun  to  rise  at  E, 
at  D  it  would  be  30°  high,  at  C  50°,  at  B 
70°,  and  at  A,  immediately  overhead,  90°. 
Going  down  the  other  side  its  altitude 
would  continually  decrease.  From  this  we 
learn  that  the  altitudes  of  celestial  bod- 
ies range  from  o  to  90°,  for  no  matter  in 
which  direction  we  face  the  horizon  the 
arc  of  the  sky  from  the  horizon  point  op- 
posite us  to  the  zenith,  which  is  the  point 
immediately  overhead,  will  measure  90°. 

The  first  element,  then,  required  in  any 
problem  of  navigation  by  observation,  is 
the  angular  altitude  of  the  celestial  body 
in  use.  The  measurement  of  this  altitude 
is  made  by  means  of  the  sextant,  or  an  in- 
strument of  the  sextant  family. 

The  principal  parts  of  the  sextant  are 
shown  in  the  accompanying  sketch. 

The  sliding  limb  (No.  7)  has  a  clamp  slid- 
ing along  the  arc  (No.  10).  A  screw  passes 
through  this  clamp,  and  by  tightening  it 
the  sliding  limb  is  held  firmly  in  any  posi- 
tion at  which  it  is  placed.  It  can,  however, 


1.  Mirror. 

2.  Telescope. 

3.  Horizon-glass. 


4.  Shade-glasses.  7. 

5.  Back  Shade-glasses.        8. 

6.  Handle.  o. 


-.  Sliding  limb. 
!.  Reading-glass. 
9.  Tangent  screw. 

Arc. 


be  further  moved  by  very  small  advances 
by  the  use  of  the  tangent  screw  (No.  9.) 

The  instrument  is  held  by  the  handle 
(No.  6)  in  the  right  hand,  with  the  tele- 
scope towards  the  observer's  eye.  He  must 
now  direct  the  telescope  towards  that  part 
of  the  sea  which  is  directly  beneath  the 
celestial  object  to  be  observed.  His  line 
of  sight  will  pass  through  the  horizon-glass. 
He  now  moves  the  sliding  limb  until  the 
image  of  the  celestial  body,  reflected  by 
the  mirror  (No.  i)  appears  in  the  horizon- 
glass.  He  then  tightens  the  clamp  screw, 


described  above,  and  by  means  of  the  tan- 
gent screw  (No.  9)  moves  the  sliding  limb 
just  a  little  more, 
so  that  the  image 
"  kisses  "  the  hori- 
zon, which  is  seen 
through  the  trans- 
parent half  of  the 
horizon -glass.  If 
he  can  make  the 
image  split  on  the 
two  halves  of  the 
glass,  as  in  the 
cut,  the  "contact," 
as  it  is  called,  will 
be  all  the  more 

accurate.  He  now  reads  the  angular  alti- 
tude from  the  scale  on  the  arc  of  the  sex- 
tant by  means  of  the  reading-glass.  The 
measurement  is  shown  by  a  small  vernier 
scale  which  runs  along  the  oblong  opening 
in  the  sliding  limb. 

The  arc  itself  is  divided   into  degrees 
and  sixths  of  a  degree  in  this  manner : 


HORIZON-GLASS  WITH  SUN 
"KISSING  SEA" 


a 


u. 


74 


The  vernier  is  divided  similarly,  but  its 
parts  represent  minutes  and  sixths  of  a 
minute.  To  read  the  angle  the  zero  point 
on  the  vernier  is 
59  used  as  a  starting- 
point.  If  it  exact- 
ly coincides  with 
one  of  the  lines 
on  the  scale  of  the 
arc,  that  line  gives 
the  measurement  of  the  angle  ;  thus,  in 
this  case  the  angle  is  5^°,  or  5°  30'. 

If,  however,  you  find  the  zero  point  has 
passed  a  line  of  the 

arc,  as  in  the  sec-         ff*  5* 

ond  case  shown, 
your  angle  is  more 


_     . 

|     I 


than    5°   30',  and    \\      |      I 
you   must    look     (  C\ 

along  the  vernier 

to  the  left  till  you  find  the  point  where  the 
lines  do  coincide.  Then  add  the  number  of 
minutes  and  sixths  of  a  minute  shown  on 
the  vernier  between  zero  and  the  point  of 
coincidence  to  the  number  of  degrees  and 
minutes  shown  on  the  arc  at  the  line  which 
the  vernier  zero  has  passed,  and  the  sum  will 
be  the  angle  measured  by  the  instrument. 


75 


Some  instruments  have  the  arc  cut  to 
quarters  of  a  degree,  or  15',  and  a  quad- 
rant is  cut  to  thirds  of  a  degree,  the  ver- 
nier showing  minutes  only.  The  sextant 
is  the  instrument  most  in  use.  The  stu- 
dent will  require  some  practice  before  be- 
ing able  to  take  and  read  an  altitude  of 
the  sun,  and  a  great  deal  before  he  can  do 
anything  with  the  stars.  An  hour's  prac- 
tice under  an  old  mariner,  however,  will 
do  him  more  good  than  a  hundred  pages 
of  book  instruction. 

Regulate  the  shade-glasses  to  suit  your 
eye.  Those  at  the  top  of  the  instrument 
affect  the  image  of  the  sun  only,  and  serve 
to  deaden  its  brilliancy.  The  back  shade- 
glasses  are  used  when  the  glare  on  the  wa- 
ter is  too  powerful.  You  cannot  get  a  good 
contact  with  your  eyes  dazzled. 


ADJUSTMENTS 

I.  The  mirror  must  be  perpendicular  to 
the  plane  of  the  instrument.  Set  the  slid- 
ing limb  at  60°.  Hold  the  sextant  face  up. 
Place  the  eye  nearly  in  the  plane  of  the  in- 
strument opposite  the  apex  and  look  into 


the  mirror.  If  the  image  of  the  arc  in  the 
mirror  and  the  arc  itself  show  in  one  un- 
broken line,  the  adjustment  is  correct ;  if 
the  reflected  image  is  lower,  the  glass  leans 
backward ;  if  it  is  higher,  the  glass  leans 
forward.  Straighten  the  glass  by  turning 
the  screws  at  its  back. 

II.  The  horizon-glass  must  be  perpen- 
dicular to  the   plane  of  the   instrument. 
Set  the  zero  of  the  vernier  to  the  zero  of  the 
arc.    Hold  the  sextant  almost  face  upward, 
and  look  through  the  sighting-vane  and  the 
horizon-glass  at  the  horizon.     If  the  hori- 
zon line  and  its  image  (seen  in  the  clean 
and  silvered  parts  of  the  glass)  do  not  co- 
incide, turn  the  screw  at  the  back  of  the 
glass  till  they  do. 

III.  The  horizon-glass  must  be  parallel 
to  the  mirror.     Set  the  zero  of  the  vernier 
to  the  zero  of  the  arc.     Hold  the  instru- 
ment as  in  taking  an  observation,  and  look 
at  the  horizon.     If  the  line  and  its  image 
in  the  silvered  part  of  the  horizon-glass 
coincide,  the  adjustment  is  correct ;  if  they 
do  not  show  in  an  unbroken  line,  adjust  the 
horizon-glass  by  turning  its  screw. 

IV.  The  line  of  sight  of  the  telescope 
must  be  parallel  to  the  plane  of  the  instru- 


77 


ment.  "  Screw  in  the  telescope  containing 
the  two  parallel  wires,  and  see  that  they 
are  turned  until  parallel  with  the  plane  of 
the  sextant ;  then  select  two  stars,  at  least 
90°  apart,  and  make  an  exact  contact  at 
the  wire  nearest  the  plane  of  the  instru- 
ment, and  read  the  measured  angle.  Move 
the  sextant  so  as  to  throw  the  objects  on 
the  other  wire,  and  if  the  contact  is  still 
perfect,  the  axis  of  the  telescope  is  in  its 
right  situation  and  the  telescope  adjust- 
ment is  correct.  If  the  images  have  sep- 
arated, it  shows  that  the  object  end  of  the 
telescope  droops  towards  the  plane  of  the 
sextant,  and  if  the  images  overlap,  it  proves 
that  the  object  end  of  the  telescope  points 
away  from  the  plane  of  the  instrument. 
This  will  be  rectified  by  the  screws  in  the 
collar  of  the  sextant.  A  defect  in  the  tel- 
escope adjustment  always  makes  angles 
too  great "  (Patterson). 


INDEX   ERROR 

It  is  better  to  let  your  instrument  alone 
after  once  adjusting  it.  If  you  continually 
torture  it,  you  will  get  it  hopelessly  out  of 


78 


order.  Error  remaining  after  adjustment 
is  called  index  error.  It  is  found  thus  : 
Set  the  sliding  limb  at  o,  hold  the  instru- 
ment perpendicularly,  and  look  at  the 
horizon.  Move  the  sliding  limb  forward 
or  backward  till  the  horizon  line  and  its 
image  coincide  in  the  horizon  -  glass. 
Clamp  the  sliding  limb  and  read  the  an- 
gle, which  is  the  index  error.  If  zero  on 
the  vernier  is  to  the  left  of  zero  on  the  arc, 
the  index  error  is  to  be  subtracted ;  if  it  is 
to  the  right,  the  error  must  be  added. 
Index  error  is  usually  expressed  thus :  I.  E. 
i°  15'— ;  or  I.  E.  2°8'+. 


HINTS  ON  TAKING   ALTITUDES 

Learn  to  take  a  single  sight  with  accu- 
racy. It  is  a  good  thing  to  take  the  mean 
of  three  or  four  sights  when  working  longi- 
tude, but  you  cannot  always  do  that. 

Oscillating  the  instrument  from  right  to 
left  and  back,  while  taking  a  sight,  will 
make  the  image  skim  the  horizon  so  that 
you  may  make  sure  of  the  point  vertically 
under  it. 

When  fog  obscures  the  horizon  from  the 


deck,  you  can  sometimes  get  a  new  horizon 
by  lowering  away  a  boat. 

In  rough  weather  try  to  get  the  mean  of 
three  or  four  sights.  You  thus  reduce  the 
amount  of  error  caused  by  the  pitching  of 
the  ship. 

Ascertain  the  index  error  before  taking 
every  altitude  or  set  of  altitudes.  The  er- 
ror is  liable  to  change. 


CORRECTING   THE   ALTITUDE 

Certain  corrections  have  to  be  made  to 
all  altitudes  taken  with  a  sextant.  These 
corrections  are  for  dip  of  the  horizon,  re- 
fraction, and  in  the  cases  of  the  sun  and 
moon,  for  semi-diameter. 

The  altitude  used  in  the  computation  of 
the  ship's  position  is  that  of  the  centre  of 
the  celestial  body.  As  already  explained, 
the  sextant  gives  the  altitude  of  the  upper 
or  lower  edge. 

For  navigational  purposes  we  assume 
that  the  diameter  of  the  sun  equals  32'  of 
the  arc  of  the  sky.  Therefore,  if  you  take 
the  altitude  of  the  lower  edge  you  must 
add  1 6',  or  half  the  diameter,  to  get  the 


8o 


altitude  of  the  centre.  If  you  take  the  al- 
titude of  the  upper  edge,  as  you  might 
have  to  do  in  case  the  lower  one  was  ob- 
scured by  clouds,  you  must  subtract  16'. 
Stars,  having  no  apparent  diameter,  do  not 
call  for  this  correction. 

Dip  of  the  horizon  means  an  increase  in 
the  altitude  caused  by  the  elevation  of  the 
eye  above  the  level  of  the  sea.  The  sim- 
plest illustration  of  this  is  afforded  by  the 
accompanying  figure.  If  the  eye  is  on  the 


level  of  the  sea  at  A,  it  is  in  the  plane  of 
the  horizon  CD,  and  the  angles  EAC  and 
EAD  are  right  angles,  or  90°  each.  If  the 
eye  is  elevated  above  A,  say  to  B,  it  is 
plain  that  the  angles  EBC  and  EBD  are 


greater  than  right  angles,  or,  in  other  words, 
that  the  observer  sees  more  than  a  semi- 
circle of  sky,  and  hence  all  measurements 
made  by  the  sextant  are  too  large. 

The  real  cause  of  this  phenomenon  is 
the  curvature  of  the  earth's  surface,  which 
causes  the  apparent  meeting  line  of  the 
sea  and  sky  to  extend  as  we  go  higher  up. 

The  elevation  of  the  eye  makes  the  angle 
too  great;  hence  the  correction  for  dip  is 
always  subtracted  from  the  altitude. 

Table  XIV.  gives  the  corrections  for  vari- 
ous heights  of  the  eye.  It  is  the  naviga- 
tor's business  to  measure  the  height  of  his 
eye  above  the  water-line  of  his  ship  at 
such  places  as  he  may  wish  to  stand  when 
taking  altitudes. 

Refraction  is  a  curving  of  the  rays  of 
light  caused  by  their  entering  the  earth's 
atmosphere,  which  is  a  denser  medium 
than  the  impalpable  ether  of  the  outer  sky. 
The  effect  of  refraction  is  frequently  seen 
when  an  oar  is  thrust  into  the  water  and 
looks  as  if  it  were  bent. 

Refraction  always  causes  a  celestial  ob- 
ject to  appear  higher  than  it  really  is.  This 
phenomenon  is  greatest  at  the  horizon 
and  diminishes  towards  the  zenith,  where 

6 


it  disappears.  Table  XX.  gives  the  correc- 
tions for  mean  refraction,  which  are  al- 
ways subtracted  from  the  altitudes.  In 
the  higher  altitudes,  select  the  correction 
for  the  nearest  degree. 

Avoid  taking  low  altitudes  (15°  or  less) 
when  the  atmosphere  is  not  perfectly  clear. 
Haziness  increases  refraction.  If  com- 
pelled to  take  a  low  altitude  when  there  ap- 
pears to  be  more  than  the  normal  amount 
of  refraction,  correct  the  refraction  for  the 
height  of  the  barometer  by  Table  XXL, 
Bowditch. 

The  student  should  now  be  ready  to 
take  and  correct  all  altitudes. 

Example :  At  sea,  June  27, 1894,  observed 
meridian  alt. :  O  (this  sign  stands  for  the 
sun ;  *  for  a  star)  67°  26'  1 5" ;  index  error, 
i°  15'+ ;  height  of  eye,  25  feet.  Required 
the  T.  C.  A.  (true  central  altitude). 

Ofcs.  alt.  O 67°  26'  15" 

I.  E i°  15'  oo" 

68°  41'  15" 
Semi-diam 16' 

68°  25'  15" 
H.  of  E.  correction 4"  54" 

68°  20'  21" 
Refraction 23. 6" 

T.  C.  A 68°  I9-  57.4" 


THE  CHRONOMETER 

The  chronometer  is  simply  a  finely  made 
and  adjusted  time-piece  placed  in  a  box 
and  swung  in  gimbals,  as  a  compass  is,  to 
prevent  it  from  being  injured  by  the  mo- 
tion of  the  ship. 

The  care  of  a  chronometer  is  not  essen- 
tially a  part  of  the  science  of  navigation, 
but  in  practice  the  navigator  has  to  use 
and  care  for  his  own  chronometers,  and 
the  author  has,  therefore,  in  the  latter  part 
of  this  book,  given  some  suggestions  as  to 
the  proper  treatment  of  these  instruments. 

The  purpose  of  the  chronometer  aboard 
ship  is  to  register  Greenwich  time.  Eng- 
lish and  American  navigators  reckon  their 
longitude  east  or  west  from  the  Greenwich 
meridian,  and,  as  we  shall  learn  further 
on,  the  computation  of  longitude  consists 
in  ascertaining  the  difference  between  the 
time  at  Greenwich  and  the  time  at  the 
ship. 

The  secondary  reason  for  carrying  a 
chronometer  is  that  the  astronomical  data 
contained  in  the  Nautical  Almanac  are  all 
given  for  the  hour  of  Greenwich  noon. 
The  chronometer  shows  us  how  many 


hours  before  or  after  Greenwich  noon  it  is, 
and  thus  we  are  enabled  to  reduce  the 
data  to  the  time  of  taking  the  observa- 
tion. 

It  is  customary  at  sea  to  use  a  hack 
watch,  set  to  the  time  of  the  chronometer, 
in  taking  observations^  the  chronometer 
itself  never  being  removed  from  its  place. 

Every  chronometer  gains  or  loses  a  little 
time  every  day.  When  in  port  the  instru- 
ment is  taken  to  a  maker,  who  regulates  it 
and  ascertains  its  daily  rate  of  losing  or 
gaining.  On  returning  it  to  the  owner,  the 
maker  furnishes  a  memorandum  stating 
that  on  such  and  such  a  date  the  chro- 
nometer was  so  many  minutes  and  seconds 
faster  or  slower  than  Greenwich  time,  and 
was  losing  or  gaining  so  much  a  day. 

The  navigator,  therefore,  must  correct 
the  time  shown  by  his  chronometer,  by 
adding  or  subtracting  the  daily  rate.  It  is 
obvious  that  the  daily  rate  must  be  multi- 
plied by  the  number  of  days  gone  since 
the  memorandum  was  made,  and  that  if  it 
is  a  losing  rate  it  must  be  added,  and  if  a 
gaining  rate,  subtracted. 

Example:  A  chronometer  showing  2 
Jirs.,  15  min.,  27  sec. on  Oct.  ii,was  3  min., 


85 

2o  sec.  slow  of  Greenwich  time  on  Oct.  i, 
and  its  daily  rate  is  0.8  sec.  losing.  What 
is  the  correct  Greenwich  time  ? 

Ans.  Oct.  i  to  Oct.  11=10  days;  0.8 x 
10=8.0  sec.  loss.  On  Oct.  1 1 ,  therefore,  the 
chronom.  is  3  min.,  20  sec.-|-8  sec.  slow. 

Chronom.  time 2  h.     15  m.    275. 

Correction  -f 3  m.    28  s. 

Correct  G.  T 2  h.     18  m.     55  s. 

It  is  obvious  that  the  correction  for 
daily  rate  may  be  computed  for  many  days 
in  advance.  The  navigator  must,  how- 
ever, be  sure  to  remember  to  correct  his 
chronometer  time.  If  he  fails  to  do  so, 
he  will  fall  into  serious,  perhaps  even  fatal 
errors. 


THE  NAUTICAL  ALMANAC 

The  Nautical  Almanac  is  a  book  pub- 
lished by  the  government,  and  containing 
certain  data,  computed  by  the  national  as- 
tronomers. Without  these  data  the  short 
and  simple  astronomical  problems  of  nav- 
igation cannot  be  solved. 

The  navigator  must  bear  in  mind  at  all 
times  the  fact  that  these  data  are  given  for 


86 


Greenwich  noon.  The  data  concerning 
the  sun  are  given,  under  the  heading  of 
the  month,  on  two  pages.  The  left-hand 
page  contains  the  data  for  apparent  time  ; 
the  right-hand  page  those  for  mean  time, 
The  significance  of  these  terms  will  be  ex- 
plained in  the  appropriate  place.  At  pres- 
ent it  is  only  necessary  to  say  that  when 
dealing  with  apparent  time,  you  must  take 
your  data  from  the  left-hand  page ;  and 
when  dealing  with  mean  time,  from  the 
right-hand.  Each  page  looks  like  the 
extract  which  is  reproduced  on  page  87. 
The  student  must  not  be  alarmed  by 
these  data.  They  are  much  simpler  af- 
fairs than  they  appear  to  be.  But  he 
must  understand  them  thoroughly  and 
know  how  to  handle  them  before  proceed- 
ing to  the  simplest  observation. 

Declination.  —  The  declination  of  a  ce- 
lestial body  is  its  distance  north  or  south 
of  the  equator,  measured  in  degrees.  In 
other  words,  declination  is  simply  celestial 
latitude.  The  sky  as  it  appears  to  the 
eye,  constitutes  a  sphere  surrounding  the 
earth,  as  in  the  diagram.  The  circumfer- 
ence of  this  sphere  must  contain  360°. 
Hence  if  the  sun  were  immediately  over  a 


ss 

Day  of  the  week 

January,  1895.—  AT  GREENWICH  MEAN  NOON 

+<*»- 

Day  of  the  month 

\o  oo  oo  cx»rr 

OJ  *.  M 

Apparent 
Rt.  Ascension 

The  Sun's 

vo  b  b  b  ^ 
o  o  N  <*> 

M  a 

C/3C/3C/JC/3 

K>  M  M  M 

O  O  O**© 

H 

S  ^ 

ui  ^  OJ  N 

N  "X  %  J 

j8 

m^^w  3 

S     o  W 

liffl 

Ills' 

if 

CX5  00  0000  3* 

Wt  tn  ^  *. 

tn  «  vj  w  g 

»£  J>£  „, 

?M 

c's  =•-• 

3  0  ^  3 

ILLUSTRATION  OF  DECLINATION 

point,  say  B,  it  would  be  in  lat.  19°  N.,  or, 
in  other  words,  its  declination  would  be 
19°  N. 

Declination  is,  however,  a  varying  quan- 
tity. Every  school-boy  knows  that  the  sun 
goes  south  in  winter  and  comes  north  in 
summer.  This  is  because  the  axis  of  the 
earth  is  inclined  to  the  plane  of  its  orbit. 
If  it  were  perpendicular,  the  sun  would 
always  be  immediately  over  the  equator. 


The  extreme  limits  of  the  sun's  declina- 
tion are  23°  27'  30"  north  and  south.  The 
former  point  is  reached  on  June  21,  and  the 
latter  on  Dec.  21.  Half  way  between  the 
former  and  the  latter  the  sun  crosses 
the  line,  bound  south,  as  the  sailors  say. 
Therefore  from  June  21  to  Sept.  22  or  23 
the  sun  is  in  north  declination,  which  is 
constantly  decreasing.  From  the  latter 
date  till  Dec.  21  it  is  in  south  declination, 
which  is  always  increasing.  From  Dec.  21 
till  March  21  or  22  the  sun's  south  declina- 
tion decreases,  and  from  the  latter  date  till 
June  2 1  it  is  in  north  declination,  increasing. 
These  points  are  extremely  important.  By 
remembering  them  you  can  never  be  in 
doubt  as  to  whether  the  declination  is 
north  or  south. 

It  is  obvious  that  it  is  important  for  the 
navigator  to  know  the  rate  at  which  the 
declination  changes.  This  is  found  in  the 
column  of  the  N.  A.  (symbol  for  Nautical 
Almanac]  adjoining  the  declination.  The 
first  thing  to  do  is  to  multiply  it  by  the 
number  of  hours  before  or  after  Greenwich 
noon  as  shown  by  the  chronometer,  for  the 
declination  is  given  for  noon. 

Secondly,  if  the  time  shown  is  after  noon 


and  the  declination  is  increasing,  add  the 
ascertained  variation.  If  the  declination 
is  decreasing,  subtract  the  variation.  If 
the  time  is  before  noon  and  the  declination 
is  increasing,  subtract  the  variation,  be- 
cause the  declination  will,  of  course,  be 
larger  at  noon  than  at  any  previous  hour. 
If  the  declination  is  decreasing,  add  the 
variation. 

The  result  obtained  from  any  of  these 
processes  is  called  the  corrected  declination. 
The  corrected  declination  is  always  em- 
ployed in  figuring  out  the  results  of  an  ob- 
servation. 

EXAMPLES 

At  sea,  May  18,  1894,  chronom.  showed 
3  hrs.,  15  min.,  18  sec.  P.M.  Required  the 
cor.  dec.  of  0  . 

Dec  .....  19°  36'  44.1"  N. 

Cor  ......          \'  46.4" 

Cor.  dec.  19°  38'  30.5"  N.       Hourly  diff> 
Chronom.  time.  .  3  h.  15  m.= 


60  )  io6.47oo"(i'  46.4" 
60 


At  sea,  May  18,  1894,  chronom.  showed 
10  hrs.,  30  min.,  12  sec.  A.M.  Required  the 
cor.  dec.  of  O  . 

Dec  ......  19°  36'  44.1"  N.  Chronom.  roh.  som.  125.  A.M. 

Cor  ......  49.1"  i2h.  oom.  oos.  noon 

Cor.  dec.  19"  35'  55.0"  N.  Time  before  noon,  i  h.  29  m.  48s.=r  i.$h. 
Hourly  din"  ......  32.76" 

Time  before  noon  .....  —  1.50 

163800 
3276 
Correction  ...............  49.1400" 

At  sea,  Jan.  22,  1894,  chronom.  showed  2 
hrs.,  45  min.,  oo  sec.  P.M.  Required  cor. 
dec.  of  0. 

Dec  .....  19°  36'  38.7"  S.  Hourly  var..34.6s" 

Cor  .....  i'  35.2"        Chro.  time  P.M.  ..  2.75 

Cor.  dec.  19°  35'  03.5"  S.  17325 

24255 
6930 


60 


At  sea,  Jan.  22,  1894,  chronom.  showed 
9  hrs.,  1  6  min.,  15  sec.  A.M.  Required  cor. 
dec.  of  O. 

Dec  ----  19°  36'  38.7"  S.  Hourly  var.  .34.65" 

i'35.2"  Timebef.) 
_       noon       )"____ 
Cor.  dec.  19°  38'  13.9"  S.  95-2875"=  i'  35-2" 


APPARENT   AND   MEAN   TIME — THE 
EQUATION 

Apparent  time  is  that  shown  by  the  sun. 
Mean  time  is  that  shown  by  the  clock. 

The  equation  of  time  is  the  difference 
between  them. 

The  earth  revolves  on  its  axis  once  in  24 
hours,  and  theoretically  the  sun  crosses 
the  meridian  of  any  given  place  at  pre- 
cisely 12  o'clock  each  day,  and  it  is  then 
noon.  As  a  matter  of  fact  this  is  not  so. 
The  earth  does  not  revolve  at  a  uniform 
rate  of  speed,  and  consequently  sometimes 
the  sun  is  a  little  ahead  of  time  and  again 
it  is  behind. 

Now  you  cannot  manufacture  a  clock 
which  will  run  that  way.  Its  hours  must 
all  be  of  exactly  the  same  length,  and  it 
must  make  noon  at  precisely  12  o'clock 
every  day.  Hence  we  distinguish  clock 
time  from  sun  time  by  calling  the  former 
mean  (or  average)  time  and  the  latter  ap- 
parent. 

Your  chronometer  shows  G.  M.  T. 
(Greenwich  mean  time). 

Your  cabin  clock  should  show  L.  M.  T. 
(Local  mean  time). 


The  sun  always  gives  L.  A.  T.  (local  ap- 
parent time.) 

Hence,  if  you  wish  to  add  sun  time,  as 
ascertained  from  an  observation,  to  G.  M. 
T.,  you  must  convert  the  former,  L.  A.  T., 
into  L.  M.  T.  by  applying  the  equation  of 
time. 

In  some  operations  you  must  convert 
G.  M.  T.  into  G.  A.  T.,  which  is  also  done 
by  applying  the  equation. 

Directions  are  given  at  the  top  of  the 
column  in  the  N.  A.  as  to  adding  or  sub- 
tracting the  equation.  If  a  black  line  is 
drawn  across  below  the  direction,  look  for 
a  similar  line  in  the  equation  column.  If 
you  add  above  the  line,  you  subtract  be- 
low, and  vice  versa. 

The  equation  is  subject,  like  declination, 
to  hourly  variation.  This  is  found  in  the 
column  to  the  right  of  the  equation.  It  is 
applied  to  the  equation  precisely  as  the 
variation  for  declination  is  applied  to  it. 
If  the  time  is  after  noon  and  the  equation 
is  increasing  (which  you  can  tell  by  in- 
spection of  the  column),  add  the  correc- 
tion ;  if  decreasing,  subtract.  Before  noon 
reverse  these  processes. 

Example:  At  sea,  Feb.  27,  1882,  chro- 


nom.  showed  4  hrs.,  26  min.,  15  sec.  P.M. 
Required  G.  A.  T. 

G.  M.  T 4  h.  26  in.  15  s.  P.M         Hourly  var.  of  equation. .  .0.456" 

Cor.  equat..          12  m.  55.95.  Time  after  noon 4.5 

G.A.T 4h.  13  m.  19.15. 


Cor.  equat 12  in.  55.97  s. 


The  student  will  observe  that  in  making 
these  corrections  it  is  very  convenient  to 
use  hours  and  decimal  fractions  of  hours. 
Remember  that  6  minutes  are  .1  of  an 
hour ;  6  sec.  =  .1  min.  For  instance,  4  hrs., 
42  min.  =4.7  hrs. ;  4  hrs.,  15  min.,  =  4.25 
hrs.  In  making  the  correction  for  decli- 
nation it  is  not  necessary  to  trouble  your- 
self about  a  minute  of  time  more  or  less. 
In  correcting  the  equation,  especially  when 
you  come  to  longitude  observations,  be  ac- 
curate, for  every  second  counts. 


LATITUDE   BY   MERIDIAN   ALTITUDE 

A  meridian  altitude  is  one  taken  when 
the  celestial  body  observed  bears  true 
south  or  north  of  the  observer,  or  is  pre- 
cisely above  the  meridian  of  longitude  on 


95 


which  he  stands.  In  the  case  of  the  sun 
this  is  at  apparent  noon. 

A  meridian  altitude  gives  the  most  ac- 
curate latitude,  for  reasons  which  will  here- 
after be  explained. 

The  general  formula  for  a  meridian  alti- 
tude is  lat.  =  zenith  distance  +  or  — •  dec- 
lination. 

Zenith  distance  is  the  distance,  measured 
in  degrees,  from  the  point  precisely  over 
the  observer's  head  to  the  observed  body. 
Let  us  suppose  that  you  and  the  sun  are 
both  north  of  the  equator.  If  now  you 
can  ascertain  exactly  how  far  you  are  north 
of  the  sun,  and  how  far  the  sun  is  north  of 
the  equator,  you  will,  by  adding  the  two 
measurements  together,  know  your  lati- 
tude. 

The  declination  of  the  sun,  obtained 
from  the  N.  A.  and  corrected  for  chro- 
nom.  time,  as  already  explained,  is  the  dis- 
tance of  the  sun  from  the  equator. 

The  zenith  distance  is  the  difference  be- 
tween the  altitude  of  the  sun,  taken  by 
the  sextant,  and  90°.  You  know  that  it  is 
90°  from  the  zenith  to  the  horizon.  Hence, 
having  got  the  altitude  of  the  sun,  you 
have  only  to  subtract  it  from  90°  to  find 


how  far  you  are  from  the  sun.     The  arc 
DBC  in  the  diagram  measures  90°.     If  the 
sun  is  at  B,  it  is  48° 
-.«?•  from  C,  the  horizon, 

^x\*  and  42°  from  D,  the 

^  zenith. 

\  Now  if  you  are  42° 

\£       north  of  the  sun,  and 
1       it  is  10°  north  of  the 
>.  •       equator,  you  must  be 

-*g     52°  north  of  the  equa- 
tor, or  in  lat.  52°  N. 

That  is  the  first  and  simplest  case.  Sup- 
pose, however,  the  sun  is  in  south  declina- 
tion, and  you  are  somewhere  in  north  lat- 
itude. In, that  case  your  distance  north 
of  the  equator  would  naturally  be  the  ze- 
nith distance  minus  the  declination,  be- 
cause the  zenith  distance,  altitude,  and  dec- 
lination together  would  make  an  arc  of 
over  90°,  and  you  can't  be  over  90°  north 
or  south  of  the  equator. 

Again,  suppose  that  the  sun  is  in  22° 
south  declination,  and  you  are  10°  north  of 
the  sun.  In  that  case  you  would  have  to 
subtract  the  zenith  distance  from  the  dec- 
lination to  get  your  latitude,  because  the 
sun's  latitude  is  greater  than  yours.  From 


97 


these  considerations  we  deduce  the  fol- 
lowing rule : 

Begin  to  measure  the  altitude  of  the  sun 
with  the  sextant  a  short  time  before  noon. 
The  altitude  will  constantly  increase  till 
apparent  noon,  when  it  will  stop  and  then 
begin  to  decrease.  You  will  be  able  to  de- 
tect this  by  bringing  down  the  image  of 
the  sun  to  the  horizon  in  the  horizon-glass 
and  carefully  watching  it.  The  highest 
altitude  attained  is  the  one  you  need.  At 
that  instant  note  the  chronometer  time, 
and  report  8  bells  to  the  captain. 

To  work  out  the  lat.,  call  the  altitude  S. 
if  the  sun  is  south  of  you,  N.  if  north. 
Correct  the  altitude  for  semi-diam.,  dip, 
and  refraction  as  already  explained.  Sub- 
tract the  true  central  alt.  from  90°  to  ob- 
tain the  zenith  dist.  If  the  alt.  is  S.,  name 
Z.  D.  north,  or  vice  versa.  Correct  the  dec- 
lination for  the  chronom.  time  as  already 
explained.  If  Z.  D.  and  dec.  are  both  N. 
or  both  S.,  add  them,  and  the  sum  will  be 
the  lat.  N.  or  S.  as  indicated.  If  one  is  N. 
and  the  other  S.,  subtract  the  less  from  the 
greater,  and  the  answer  will  be  the  lat. 
named  N.  or  S.  after  the  greater. 

7 


EXAMPLES 

At  sea,  June  15,  1894.  Observed  merid. 
alt.  Q,  lower  limb,  71°  i5'oo"S.  Index 
error, —47';  height  of  eye,  25  ft.;  chro- 
nom.  3  hrs.,  28  min.,  15  sec.  P.M. ;  chronom. 
slow  of  G.  M.  T.  i  min.,  50  sec.,  on  June  5. 
Daily  rate,  —.5  sec.  Required  lat.  of  ship. 


70*    28'  OO" 

Semi-diam 16'  oo" 

70*  44'  oo" 
4'  54" 


Chronom....  3  h.  28m.  155.  P.M. 
Correction..  im.  555. 

3h.  30  m.  10 s.  P.M. 

Hourly  var 6.14" 

Time  after  noon 3.5 


Dip ,_ 

70°  39'  06" 
Refraction . 20" 

T.  C.A .70°  38'  46" 

90    cor  ocf' 

Z.D 19°  21'  14"  N.      Dec 23*  I97  59"  N. 

Correct  dec .23'  2c/  20"  N.      Correction 21" 

Lat 42"  41'  34"  N.      Correct  dec 23°  20'  20"  N. 


Correction 21.490" 


At  sea,  Sept.  25,  1894.  Observed  merid. 
alt.  0  ;  lower  limb,  50°  3'  oo"  S. ;  index 
error,  -j-i°  14' ;  height  of  eye,  20  ft. ;  chro- 
nom. 2  hrs.,  15  min.,  10  sec.  P.M.  ;  chronom. 
slow  of  G.  M.  T.  on  Sept.  20,  i  min.,  10  sec. ; 
daily  rate,  — .3  sec.  Required  the  lat.  of 
ship. 


99 


Obs.  alt.  Q 50"  03'  oo"  S.    Chronom  —  2  h.  15  m.  10  s.  P.M. 

I.E.  -H i°  14'  oo"        Cor.  for  Sept.  25  h.    im.  11.55. 


51°  17'  oo" 
...        ID'OO" 

G.  M.  T.... 

.  2h.  i6m.  21 

.55.  P.M. 

«°  «'  oo" 

Hourly  var 

38  53" 

H.  ofE.  cor.... 

..         34'23" 

G.M.T.... 

2.25 

Refraction  

29265 
11706 

T.  C.  A  
Z.  D  .  .  . 

...51°  27'  5o" 
90    oo'  oo" 
...38°  32'  io"N. 

I2O 

201.  us. 

Lat 37°  3?  02"  N.       Dec o°  56'  57"  S. 

Correction o"    2'  n" 

Cor.  dec 59'  08"  S. 

The  operation  can  be  shortened  a  little 
by  making  the  corrections  in  a  mass,  using 
the  refraction  given  for  the  observed  alt., 
as  shown  in  the  remaining  examples. 

At  sea,  June  20, 1894.  Observed  merid. 
alt.  O  86°  29'  45"  N.  No  index  error ; 
height  of  eye,  20  ft. ;  chronom.  10  hrs.,  26 
min.,  30  sec.  A.M.;  chronom. fast  of  G.  M.T. 
on  date  3  min.,  21  sec.  Required  lat.  of  ship. 

Semi-diam 16'  oo"-f-  Hourly  var 0.99" 

Dip 4'  23" —  Time  before  noon 1.4 

Refraction 4" —  "396 

Correction 1 1'  33"-)-  99 

Correction 1.386" 

Obs.  alt. . .  86°  29'  45"  N.  Dec 23°  27'  07.  i"  N. 

Cor n"  33"  Cor 1.3" 

T.  C.  A  .  .86°  41'  18"  N.  Cor.  dec.. 23°  27'  05.8"  N. 
90°  oo'  oo" 

Z.  D ~3°~i8'~42*~S. 

Cor.  dec.. 23°  27'  05.8"  N. 
Lat 20°  08'  23.8"  N. 


In  actual  sea  practice  so  small  a  correc- 
tion as  1.3"  would  not  be  applied  to  the 
dec.,  because  it  has  no  effect  on  the  result- 
ing lat.  It  would  be  necessary  in  estab- 
lishing a  geographical  location,  such  as 
that  of  a  light.  Working  to  tenths  of  sec- 
onds is  also  rarely  necessary  in  lat.  prob- 
lems. Lat.  is  generally  expressed  simply 
in  degrees  and  minutes,  because  at  sea  it 
is  sufficient  to  know  your  position  within 
a  mile.  The  preceding  problem,  in  prac- 
tice, would  be  worked  thus : 

Semi-diam 16'  oo" 

Dip 4'  23;; 

Refraction 4 

Correction n'  33" 

Obs.  alt 86°  *<)%'  N. 

Correction 11%' 

T.C.A 86°  41*' 

90°  oo' 


Z.D 3°  iS^'S. 

Dec 23°  27'  N. 

Ltt 2o°o8*'N 


The  difference  between  J  minute  (15") 
and  23"  is  of  no  account  at  sea.  Hence, 
when  the  chronom.  time  from  noon  and 
the  hourly  variation  of  the  dec.  are  both 
small,  no  correction  need  be  applied  to  the 
dec.  If  either  one  or  the  other  is  large,  al- 


ways  apply  the  error.  Many  licensed  mas- 
ters never  apply  it.  Do  not  follow  any  such 
leaders,  or  you  will  some  day  land  on  a 
rock  which  you  think  is  six  or  eight  miles 
north  or  south  of  you.  When  approaching 
the  land  carry  out  your  work  to  fractions ; 
you  cannot  then  be  too  accurate. 

Another  popular  folly  with  merchant 
skippers  and  yacht  captains  is  to  regard 
the  correction  to  the  alt.  as  a  constant 
quantity  of  12'+.  Instead  of  adding  it  to 
the  alt.  and  then  subtracting  the  sum  from 
90°,  they  make  a  short  cut  and  subtract  the 
12'  from  90°,  getting  a  constant  of  89°  48', 
from  which  they  always  subtract  the  alt. 
They  would  work  the  last  example  thus: 

Constant 89°  48' 

Obs.  alt 86°  29%' 

Z.  D 3C  iW 

Dec 23°  27' 

Lat ., * 20°  08%' N. 

That  looks  short  and  easy,  and  the  dif- 
ference is  only  £  mile.  But  let  us  take 
another  case.  On  Dec.  20,  1894,  your  obs. 
merid.  alt.  was  n°  34'  oo"  S. ;  no  index 
error;  height  of  eye,  30  ft.;  chronom,  u 
Jirs.,  oo'  oo"  A.M, 


Right  way  Wrong  way 

Semi-diam. . .  16'  00"+  Constant .  .89°  48' 

Dip 5'  22"—  Obs.  alt...  11°  34  S. 

Refraction  . . .  4'  36"-  z  D 7go  ,4'  N. 

Correction —  6'  02"-!-  Dec .23°  26%'  S. 

Obs.  alt.  0. . .  11°  34'  S. 

Correction 6'-f- 

T.  C.  A 11°  40' 

90°  oo' 

Z.  D 78°  20'  N. 

Dec 23°  26%'  S. 

Lat 54°  53^'N. 

The  student  will  note  that  the  89°  48' 
puts  the  latitude  6'  in  error :  and  it  fails 
just  at  the  time  when  accuracy  is  most 
needed — in  winter.  The  cause  of  the  error 
is  the  failure  to  allow  for  dip  and  refrac- 
tion. 


LATITUDE  BY   MERIDIAN   ALTITUDE  OF 
A   STAR 

The  student  should  purchase  a  set  of 
simple  star  maps,  and  acquaint  himself 
with  the  location  of  the  principal  fixed 
stars.  Having  learned  to  know  the  stars, 
he  should  practise  assiduously  at  taking 
their  altitudes.  The  best  hours  for  ob- 
servation are  morning  and  evening  twi- 
lights, when  the  horizon  is  clearly  defined. 


•03 


Moonlight  nights  also  bring  out  a  good 
horizon.  With  practice  and  a  first -class 
sextant,  fitted  with  a  star  telescope  and 
well  -  silvered  mirrors,  the  student  will  in 
time  learn  to  "  shoot "  stars  on  any  clear 
starlight  night. 

It  is  of  inestimable  value  to  know  how 
to  use  the  stars.  The  sun  may  be  over- 
clouded at  noon — or  all  day — and  at  dusk 
there  may  be  a  star  on  your  meridian  to 
give  you  the  latitude.  You  can  find  stars 
on  the  meridian  at  various  hours  of  the 
night,  and,  the  altitude  once  secured,  the 
rest  is  even  easier  than  working  out  lat. 
from  the  sun. 

The  declinations  of  all  the  stars  availa- 
ble for  the  navigator  are  to  be  found  in 
the  back  part  of  the  N.  A.,  in  the  star  tables. 
Those  marked  +  are  N.,  those  —  are  S. 
The  annual  variation  of  declination  is  so 
small  that  the  dec.  is  not  corrected ; 
hence  the  chronometer  time  is  not  taken, 
and  no  allowance  has  to  be  made  for  semi- 
diameter.  With  these  exceptions  the 
method  of  working  out  the  lat.  by  a  star's 
merid.  alt.  is  the  same  as  that  for  the  sun. 
You  can  tell  when  the  star  is  approaching 
the  meridian  by  its  bearing. 


Example :  At  sea,  Dec.  7,  1894.  At  10.50 
P.M.  took  merid.  alt.  *  Aldebaran  (a  Tauris) 
75°2i'oo"S;  no  index  error;  height  of  eye, 
20  ft. 

Obs.  alt.  *  . .  .75°  21'  oo"  S.          Dip 4"  23" 

Cor V  38"  Ref 15" 

T.  C.  A 75°  16'  22"  Correction 4'  38" 

90°  oo'  oo'' 

Z.D 14°  43'  38"  N. 

Dec 1 6°  17'  45"  N. 

Lat 31°  01'  23"  N. 

Nothing  in  the  shape  of  a  calculation 
could  be  much  simpler  than  that.  The 
practical  part  of  the  operation  can  be  sim- 
plified, however,  by  knowing  one  or  two 
additional  facts.  In  the  first  place,  you 
need  to  know  how  to  find  out  what  star 
you  can  use  at  a  particular  hour.  For  this 
you  must  employ  the  right  ascension  of 
the  sun  and  the  right  ascension  of  the 
star  required.  The  meaning  of  the  term 
right  ascension,  designated  R.  A.,  will  be 
explained  later.  The  R.  A.  of  the  sun  is 
to  be  found  on  the  same  page  as  the  dec. 
in  the  N.  A.  The  R.  A.  of  the  star  is  to 
be  taken  from  the  star  table. 

Subtract  the  sun's  R.  A.  from  that  of 
the  star.  If  the  latter  is  the  smaller,  add 


24  hours  to  it.  The  remainder  will  be  the 
time  of  the  star's  meridian  passage. 

To  know  which  star  will  cross  the  merid- 
ian after  a  certain  hour,  add  that  hour  to 
the  sun's  R.  A.  The  sum  will  be  the  R.  A. 
of  your  own  meridian.  If  it  is  more  than  24 
hours,  subtract  24  hours  from  it.  The  star 
table  will  then  show  you  what  star's  R.  A. 
is  equal  to  or  a  little  greater  than  your  own. 
That  will  be  the  next  star  to  cross  your 
meridian.  If  you  are  sailing  to  the  eastward, 
it  will  cross  a  little  ahead  of  time;  if  you 
are  going  west,  it  will  be  a  little  behind. 

The  next  thing  to  do  is  to  set  your  sex- 
tant at  about  the  altitude  the  star  will  at- 
tain at  its  meridian  passage,  and  at  the 
proper  time  direct  your  instrument  toward 
the  south  or  north  point  of  the  horizon. 
The  image  of  the  star  will  at  once  appear  in 
the  horizon-glass,  and  you  will  have  only  a 
few  minutes  of  watching  for  the  merid.  alt. 

To  calculate  a  merid.  alt.  subtract  your 
lat.  by  D.  R.  from  90°.  Call  the  remainder 
co-lat.,  and  mark  it  N.  or  S.  the  same  as  the 
lat.  If  the  co-lat.  and  the  dec.  are  of 
the  same  name,  add  them ;  if  of  different 
names,  subtract.  The  result  is  the  approx- 
imate merid.  alt. 


io6 


Example:  At  sea,  Aug.  29,  1894.  Desired 
to  correct  the  lat.  by  D.  R.  by  a  star  merid. 
at  9  P.M. 

R.  A.  Q loh.  31  m.  303. 

Time  at  ship gh.  oom.  oos. 

R.  A.  Meridian..  19 h.  31  m.  303. 

R.  A.  *  Altair...   19 h.  45 m.  363.  by  star  table. 

R.  A.  Altair 19  h    45  m.  36  s. 

R.  A.  Sun ich.  3im.  303. 

Time  of  ^'s  merid.  alt. .  gh-   14111.  06  s- 

Lat.  by  D.  R 45°  38'  oo"  N. 

90°  oo'  oo" 

Co-lat ."44°  22'  oo"  N. 

Dec.  Altair 8°  35'  18"  N. 

Approx.  merid.  alt 52°  57'  18" 

You  will  know  whether  the  star  is  north 
or  south  of  you  by  its  dec.  If  you  are  in 
north  lat.,  the  star  will  be  S.  of  you  if  its 
dec.  is  S.,  or  if  its  dec.  is  north  and  less 
than  your  lat.  If  its  dec.  and  your  lat.  are 
both  N.,  and  the  former  is  the  greater,  the 
star  will  be  north  of  you.  The  same  prin- 
ciple applies  if  you  are  in  S.  lat. 

Captain  Lecky  notes  that  sometimes  you 
can  get  two  stars,  one  north  and  one  south, 
almost  at  the  same  time.  Always  take  ad- 
vantage of  such  a  chance,  for  it  lessens  the 
range  of  error  to  take  the  mean  of  two  obser- 
vations. Suppose  one  star  gave  lat.  48°  1 5' 
N.,  and  the  other  gave  48°  10'  N.  The  mean, 
48°  12'  30"  N.  would  be  pretty  nearly  correct. 


LATITUDE   BY   MERIDIAN   ALTITUDE  OF 
A   PLANET 

The  mean  time  of  passing  the  meridian 
and  the  declinations  of  the  planets  are 
given  in  the  N.  A.  in  the  latter  part.  The 
dec.  has  to  be  corrected  in  the  case  of  a 
planet,  as  it  changes  quite  rapidly.  The 
almanac  gives  the  dec.  for  each  day  of 
the  month  and  the  variation  for  one  hour, 
as  in  the  case  of  the  sun.  The  remainder 
of  the  operation  is  the  same  as  that  for  a 
star. 

Example:  At  sea,  Feb.  28,  1895.  Obs. 
mend.  alt.  Saturn,  75°  21'  oo"  S. ;  no  index 
error;  height  of  eye,  20  ft.;  G.  M.  T.,  12 
hrs.,  5  min.,  oo  sec.  A.M. 

Obs.  alt.  Sat.. 75°  21'  oo"  S.       Dip 4'  23" 

4    38"  Ref 15^ 

T.  C.  A 75°  16'  22"  Cor 4'  3»" 

90°  oo'  oo" 

Z.  D 14°  43'  38"  N. 

Dec 11°  2$'  4*-9"  S. 

Lat 3°  17'  56.1"  N- 

Hourly  diff.  dec.  Feb.  27 1.60" 

Time  after  noon 12 

Correction 19.20" 

Dec.  Feb.  27 1 1°  26'  01.  i"  S. 

Cor 19.3" 

Cor.  Dec.. n°  25'  ^iV^S. 


LATITUDE   BY   MERIDIAN   ALTITUDE   OF 
THE   MOON 

The  moon  is  more  or  less  of  a  nuisance, 
and  is  not  used  by  expert  navigators  when 
it  can  be  avoided.  The  declination  changes 
so  rapidly  that  even  minutes  of 
time  have  to  be  taken  into  ac- 
count, and  one  is  likely  to  be  de- 
ceived as  to  its  semi-diameter  be- 
cause of  irradiation,  which  makes 
the  moon  at  times  look  larger 
than  it  is.  Furthermore,  in  using 
the  moon  we  have  to  allow  for 
parallax. 

Parallax  is  the  difference  in  the 


9 


angular  altitude  of  a  ce- 
lestial body  as  measured 
from  the  surface  or  the 
PARALLAX  centre  of  the  earth.     It 

is  greatest  when  the  body 
is  in  the  horizon,  and  disappears  when  it 
is  at  the  zenith.  The  sun  is  so  far  away 
that  its  parallax  never  exceeds  9".  The 
stars  have  practically  none  at  all  from  the 


109 


earth's  surface.  The  moon,  however,  is 
near  enough  to  make  an  allowance  neces- 
sary. Hence  the  rule  for  working  out  the 
moon's  merid.  alt.  is  as  follows : 

Find  the  G.  M.  T.  of  the  moon's  merid. 
passage  in  page  iv.  of  the  N.  A.  for  the 
month.  If  you  are  west  of  Greenwich  add 
the  diff.  for  the  number  of  hours  west ;  if 
east,  subtract.  The  hourly  diff.  is  given 
under  "  Upper  Transit."  (How  to  tell  the 
number  of  hours  east  or  west  will  be  ex- 
plained under  a  subsequent  heading.)  Take 
the  alt.  in  the  usual  way,  and  correct  it  for 
semi-diameter,  dip,  and  refraction.  Semi- 
diameter  must  be  taken  from  page  iv.,  N.  A. 
Take  the  moon's  parallax  from  p.  iv.,  N. 
A.,  and  correct  it  for  hourly  diff.  With 
the  corrected  parallax  enter  Table  XXIV., 
Bowditch,  and  take  therefrom  the  correc- 
tion to  be  added  to  the  altitude.  Find  the 
dec.  for  the  day  and  hour  (G.  M.  T.)  in  pp. 
v.-xii.  for  the  month,  N.  A.,  and  correct  for 
the  number  of  minutes  over  the  hour. 
Subtract  the  alt.  from  90°  to  get  Z.  D.,  and 
apply  the  moon's  corrected  dec.,  according 
to  rule  given  for  sun,  to  get  lat. 

Example:  At  sea,  May  i,  1895.  Long. 
45°  W.  =  3  hrs. ;  obs.  merid.  alt.  of  moon, 


3o°i5'oo"N.;  I.  E.  (index  error),  -|- 20';  H.of 
E.  (height  of  eye),  30  ft.;  chronom.  time,  8 
hrs.,  58  min.,42  sec.  P.M.  ;  chronom.  slowof 
G.  M.  T.  i  minute.  (See  table  on  next  page.) 


MERIDIAN   ALTITUDE   BELOW   THE   POLE 

It  is  frequently  possible  to  get  an  alti- 
tude of  a  star  when  it  is  crossing  the  me- 
ridian below  the  pole.  The  north  pole  of 
the  heavens  is  marked  very  closely  by  the 
polestar,  which  is  never  more  than  i°  20' 
distant  from  the  pole.  The  stars  in  the 
northern  part  of  the  heavens  apparently 
revolve  around  the  pole,  as  may  be  plainly 
seen  in  the  case  of  the  constellation  known 
as  the  "  Dipper."  When  the  given  star  is 
directly  under  the  pole  it  is  on  the  merid- 
ian, and  will  give  the  latitude  just  as  cor- 
rectly as  when  directly  above  it. 

When  in  very  high  latitudes,  where  the 
sun  does  not  set  during  six  months  of  the 
year,  the  same  thing  may  be  done  with  the 
sun. 

The  rule  is  a  simple  one.  It  reads  :  polar 
distance  -f-  alt.  =  lat.  Polar  distance  is  the 
distance  of  a  celestial  body  from  the  pole. 


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If  the  pole  and  the  celestial  body  are  in 
the  same  kind  of  lat.,  either  north  or  south, 
you  can  find  the  P.  D.  by  subtracting  the 
body's  declination  from  90°.  It  is  90°  from 
the  pole  to  the  equator.  If,  therefore,  the 
body  is  20°  north  of  the  equator,  it  is  70° 
south  of  the  north  pole.  But  from  the 
south  pole  it  would  be  90°  +  20°  =  1 10°. 
But  you  could  not  then  get  an  alt.  below 
the  pole,  because  when  in  that  position  the 
body  would  be  below  your  horizon.  If  you 
are  in  S.  lat.,  you  reckon  polar  distance 
from  the  south  pole. 

In  taking  an  altitude  below  the  pole,  bear 
in  mind  that  the  altitudes  continually  de- 
crease, and  that  the  lowest  is  the  merid.alt. 

Example :  Oct.  2,  1895,  obs.  alt.  a  Ursa 
Majoris  (a  of  the  Dipper),  8°  i5'oo"  N.,  be- 
below  pole ;  H.  of  E.,  10  ft. ;  no  I.  E. 

Obs.  alt.  *  ...  8°  15'  oo"      Dip 3'  06" 

Cor 9'  28"       Ref 6'  22" 

T.  C.  A 8°  05'  32"      Cor 9^28'' 

P.  D 27°  40'  56" 

Lat 35°  46'  28"  N. 

Dec 62°  19'  04"^  N. 

90°  oo'  oo" 

P.  D 27°  40'  56" 

To  set  a  sextant  for  a  merid.  alt.  below 
the  pole,  subtract  the  star's  P.  D.  from  the 


lat.  by  D.  R. ;  the  remainder  will  be  the  ap- 
proximate alt. 


LATITUDE   BY   EX-MERIDIAN   ALTITUDE 
OF  THE  SUN 

Before  proceeding  further  the  student 
should  learn  how  to  convert  longitude  into 
time  and  time  into  longitude.  The  former 
operation  will  enter  into  most  of  the  cal- 
culations yet  to  come,  and  the  latter  is  al- 
ways part  of  longitude  workings. 

The  conversion  is  based  on  the  fact  that 
the  sun  takes  24  hours  to  pass  around  the 
360°  of  the  earth's  circumference.  Divide 
360  by  24  and  you  get  the  number  of  de- 
grees he  passes  in  one  hour,  viz.,  1 5°.  Hence 
1 5°  of  long.  =  i  hour,  and  i  °  rz  -j^  of  i  hour, 
or  4  minutes.  Furthermore,  15'  of  long.  = 
i  minute  of  time,  and  i'  of  long.  =-^  of  i 
minute  of  time,  or  4  seconds.  Table  VII., 
Bowditch,  gives  the  various  equalizations 
up  to  360°,  but  you  should  be  able  to  do 
without  it. 

To  convert  time  into  long. — Multiply  the 
hours  by  1 5  to  get  degrees.  Divide  the  min- 
utes by  4,  and  add  the  quotient  to  the  num- 


ber  of  degrees.  If  any  minutes  are  left  over, 
multiply  them  by  1 5.  Divide  the  seconds  by 
4,  and  add  the  quotient  to  the  minutes.  Fi- 
nally multiply  the  remaining  seconds  by  15. 
Example:  Turn  4  hrs.,  29  min.,  38  sec. 
into  long. 

4  4)29(7°  4)38(9' 

.11  J12  J* 

60  1X15  =  15'  2X15  =  30" 

7  9" 

67°  24' 

Ans.  67°  24'  30". 

To  convert  long,  into  time. — Multiply  each 
member  of  the  quantity  by  4  and  divide  by 
60,  adding  any  figures  left  over  to  the  result 
obtained  from  the  next  number  to  the  right. 

Example :  Turn  50°  40'  15"  into  time. 
50°  40'  15" 

4    h.  1      m.  m.  *       s.  s. 

60)200(3  60)160(2  +  20  =  22  60)60(1+40  =  41 

180  120 V                                        6ov 

20  m.  40  s.                                   oo 

Ans.  3  hrs.,  22  min.,  41  sec. 

It  is  from  this  convertibility  of  time  into 
degrees  and  parts  of  degrees  (and  vice  versa) 
that  we  get  the  expression  hour-angle. 

Hour-angle  is  the  distance  of  a  body  east 
or  west  of  the  observer's  meridian,  ex- 
pressed either  in  time  or  angle.  Thus  at 
ii  A.M.  the  sun's  hour-angle  is  either  i 


hour  or  1 5°  E.,  at  i .  1 5  P.M.  it  is  either  i  hour 
and  15  min.  or  18°  45'  W. 

Now  we  come  to  ex-meridian  altitudes. 
Suppose  that  at  12  o'clock,  apparent  time, 
the  sun  is  obscured  by  clouds,  and  you 
cannot  get  your  meridian  altitude,  but  five 
minutes  later  it  is  perfectly  clear.  It  is 
possible,  fortunately,  to  use  it  even  then. 
In  fact,  you  may  work  the  ex -meridian 
problem  from  13  minutes  before  till  13 
minutes  after  noon,  but  you  must  know 
your  longitude  accurately. 

If  you  know  the  longitude,  you  can  com- 
pute the  hour-angle,  and  if  you  know  that, 
you  can  reduce  the  altitude  to  what  it 
would  be  at  noon  by  applying  the  rule 
that  near  the  meridian  the  altitude  varies 
as  the  square  of  the  interval  from  noon. 
Table  XXVI.,  Bowditch,  gives  the  change 
of  altitude  in  i  minute,  and  Table  XXVII. 
gives  the  squares  of  the  intervals  up  to  13 
minutes.  If  you  know  the  interval,  or  hou r- 
angle,  all  you  have  to  do  is  to  multiply  the 
change  for  i  minute  by  its  square,  and  add 
the  result  to  your  T.  C.  A.,  which,  either  be- 
fore or  after  precise  noon,  must  be  just  that 
much  too  low.  Hence  we  get  this  rule  : 

Take  the  chronom.  time  of  the  observa- 


II* 


tion.  Correct  it  for  rate,  as  usual.  Cor- 
rect the  chronom.  time  for  long,  by  sub- 
tracting from  it  your  long,  expressed  in 
time  if  long,  is  W.,  and  adding  if  long,  is 
E.  Result  is  local  mean  time.  Convert 
this  into  local  apparent  time  by  applying 
the  corrected  equation  of  time,  as  already 
explained.  If  the  L.  A.  T.  is  more  than  12 
hours,  the  surplusage  is  the  hour  -  angle 
west.  If  less,  subtract  it  from  12  hours, 
and  the  remainder  is  the  hour-angle  east. 
Enter  Table  XXVI.  with  the  dec.  of  the 
sun  at  the  top,  and  the  lat.  by  D.  R.  at 
the  side,  and  take  out  the  change  of  alt. 
for  i  minute.  Enter  Table  XXVII.  with 
the  hour-angle,  applying  minutes  at  the  top 
and  seconds  at  the  side,  and  multiply  the 
number  given  by  that  obtained  from  Table 
XXVI.  Mark  the  result  seconds,and  reduce 
to  minutes  if  60  or  more.  Add  this  to  the 
T.  C.  A.  to  obtain  the  merid.  alt.  Subtract 
this  from  90°  to  get  Z.  D.,  and  apply  the 
dec.  to  get  the  lat.  as  heretofore  directed. 
Example :  At  sea,  July  i  r,  1895.  Lat.  by 
D.  R.  50°  01 '  oo"  N.,  long.  40°  W.  Obs. 
ex-merid.  alt.  O  61°  45'  30".  H.  of  E.,  15 
ft. ;  I.  E.,  4' — .  Chronom.  time  (corrected) 
2  hrs.,  38  min.,  oo  sec.  P.M. 


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With  an  interval  of  time  not  greater  than 
one  hour  from  noon,  latitude  may  be  com- 
puted from  an  ex-meridian  altitude  by  what 
is  called  the  <£'  and  <£"  sight.  To  make  the 
computation  you  must  learn  to  use  Table 
XLIV.,  Bowditch.  As  this  table  is  con- 
stantly used  in  working  longitude  you 
must  make  yourself  thoroughly  familiar 
with  it. 

Table  XLIV.  contains  the  logarithmic 
sines,  cosines,  tangents,  cotangents,  secants, 
and  cosecants  for  all  angles  up  to  180°.  If 
you  have  studied  trigonometry,  you  will 
know  what  these  terms  mean.  If  you 
have  not,  you  can  use  them  just  as  well 
for  the  purposes  of  navigation.  The  top 
and  bottom  of  a  page  of  Table  XLIV. 
look  like  the  table  on  next  page. 

If  the  desired  number  of  degrees  be 
found  at  the  top,  the  name,  sine,  cosine, 
etc.,  must  also  be  found  there,  as  in  the 
cases  of  18°  and  161°  in  the  example.  If 
the  number  of  degrees  is  at  the  bot- 
tom, the  logarithmic  name  will  be  found 
there.  The  additional  minutes  must  be 
found  in  the  column  M  on  the  same  side 
of  the  table  as  the  required  degrees,  and 
tfie  logarithms  opposite  to  them.  In  apply- 


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ing  the  seconds  of  your  angle  choose  the 
logarithm  for  the  nearest  minute.  Thus, 
for  logarithms  of  10°  15'  42",  go  to  10° 
16'. 

The  columns  marked  Hour  A.M.  and 
Hour  P.M.  contain  the  apparent  time  cor- 
responding to  the  sines,  cosines,  etc.  When 
you  come  to  longitude,  you  will  have  to 
take  out  the  time  corresponding  to  sines. 
When  the  observation  is  taken  before 
noon,  you  take  the  time  out  of  the  A.M. 
column  ;  afternoon,  from  the  P.M.  Notice 
that  they  are  reversed  at  the  bottom  of 
the  page.  This  means  that  if  your  sine  is 
in  the  column  having  the  word  "sine"  at 
the  top,  you  work  from  the  top  of  the  page 
down ;  if  your  sine  is  in  the  column  with 
"  sine  "  at  the  bottom,  you  read  from  the 
bottom  of  the  page  up. 

The  parts  of  the  sines,  etc.,  to  the  left 
of  the  decimal  mark  are  called  the  index- 
es. If  the  index  is  10,  omit  it  in  adding 
the  figures.  Thus,  if  you  were  required  to 
add  the  secant  of  18°  03'  to  the  cosine  of 
71°,  you  would  have  10.02192  +  9.51264  = 
9-53456.  To  simplify  calculations,  omit  the 
index  10  when  taking  out  the  logarithm  in 
the  first  place. 


The  use  of  the  proportional  parts  of  the 
columns  A,  B,  and  C  may  be  omitted  until 
we  come  to  chronometer  sights.  We  are 
now  ready  to  give  the  rule  for  the  <p'  and 
(p"  sight. 

Take  the  chronometer  time  of  the  ob- 
servation, and  compute  the  hour-angle  of 
the  sun  as  already  explained.  Convert  the 
hour-angle  to  terms  of  degrees,  minutes, 
and  seconds.  Add  the  secant  of  the  hour- 
angle  to  the  tangent  of  the  corrected  dec- 
lination, and  the  sum  will  be  the  tangent 
of  an  arc,  which  take  out  and  call  it  <£". 
Add  the  sine  of  the  arc  <£"  to  the  cosecant 
of  the  corrected  dec.  and  the  sine  of  the 
T.  C.  A.  The  sum  will  be  the  cosine  of 
an  arc  to ,  be  taken  out  and  marked  <£'. 
The  lat.  of  the  ship  (at  the  time  of  ob- 
servation, not  at  noon)  is  either  the  sum 
or  difference  of  <£'  and  <£".  Use  the 
value  which  comes  nearest  to  the  lat.  by 
D.  R. 

Example:  At  sea,  June  8,  1895.  Posi- 
tion by  D.  RM  lat.  28°  40'  N.,  long.  60°  15' 
W.  Obs.  alt.  of  sun's  lower  limb,  after  noon, 
78°  30'  oo".  G.  M.  T.,  4  hrs.,  44  min.,  30 
sec.  P.M.  ;  H.  of  E.,  20  ft. 


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The  advantage  of  this  method  is  that 
it  is  independent  of  the  lat.  by  D.  R.,  which 
may  be,  and  frequently  is,  much  in  error. 
The  method  can  be  used  for  all  celestial 
bodies,  as  hereafter  explained. 


LATITUDE   BY  THE  POLESTAR 

Before  attacking  the  method  of  comput- 
ing lat.  by  Polaris,  the  north  star,  the  stu- 
dent may  as  well  learn  several  more  astro- 
nomical facts,  some  of  which  demand  close 
study  for  their  comprehension.  He  has 
learned  the  difference  between  mean  and 
apparent  time.  He  must  now  learn  what 
astronomical  time  and  right  ascension  are, 
and  he  may  as  well  complete  the  list  with 
sidereal  time. 

Astronomical  time  is  reckoned  from 
noon  of  one  day  to  noon  of  the  next,  and 
hence  the  astronomical  day  corresponds 
to  the  24  hours  of  a  ship's  run.  The  hours 
are  counted  from  i  to  24,  so  that  4  o'clock 
in  the  morning  o^Oct.  5  is  astronomically 
1 6  o'clock  of  Oct.  4. 

Right  ascension  is  practically  celestial 
longitude.  A  place  on  the  earth  is  located 


by  its  latitude  and  longitude  ;  a  heavenly 
body  by  its  declination  and  right  ascen- 
sion. But  R.  A.,  as  it  is  indicated,  is  not 
measured  in  degrees  and  minutes,  nor  is 
it  measured  east  and  west.  It  is  reckoned 
in  hours  and  minutes  all  the  way  around 
the  sky  from  west  to  east  through  24 
hours. 

The  celestial  meridian  from  which  this 
celestial  longitude  begins  is  not  that  of 
Greenwich,  but  it  is  that  passing  through 
the  equator  at  the  point  where  the  sun 
crosses  the  line  in  the  spring. 

When  we  speak  of  a  star  as  having  a 
R.  A.  of  3  hrs.,  42  min.,  1 5  sec.,  we  mean  that 
any  given  spot  on  the  surface  of  the  earth 
will  occupy  3  hrs.,  42  min.,  15  sec.,  in  revolv- 
ing from  the  prime  meridian  of  celestial 
long,  to  the  meridian  of  the  star. 

You  will  meet  with  the  expression  right 
ascension  of  the  meridian.  That  means 
the  R.  A.  of  the  meridian  on  which  you  are, 
and  in  many  stellar  observations  you  need 
to  know  it  in  order  to  compare  it  with  the 
R.  A.  of  the  star.  • 

It  so  happens  that  the  R.  A.  of  the 
meridian  and  local  sidereal  time  are  the 
same  thing.  Sidereal  time  is  "  star  "  time, 


125 


as  opposed  to  solar  or  "sun  "  time.  The 
sidereal  day  contains  24  hours,  but  it  does 
not  begin  at  midnight  as  the  legal  day 
does,  nor  at  noon  like  the  astronomical 
day.  It  begins  when  the  prime  celestial 
meridian  (that  at  which  celestial  longitude 
commences)  is  right  over  the  meridian  on 

R 


e*. 


EAST/ 

/ 


which  you  stand.  It  is  then  what  you 
might  call  sidereal  noon  at  your  place, 
just  as  it  is  solar  noon  when  the  sun  is  on 
the  meridian. 

Now  suppose  R.  to  be  the  prime  celes- 
tial meridian,  and  M.  your  meridian.  When 
M.  is  under  R..  sidereal  time  at  M.  begins. 


126 


Also  right  ascension  is  measured  east- 
ward in  hours  and  minutes  from  R.  Now 
if  M.  occupies  2  hrs.,  15  min.,  12  sec.  in  re- 
volving with  the  motion  of  the  earth  to 
A,  when  it  arrives  at  A  it  will  be  2  hrs., 
15  min.,  12  sec.  o'clock  sidereal  time  at  M. 
And  that  must  also  be  the  R.  A.  of  M., 
because  R.  A.  is  measured  from  the  same 
point  as  sidereal  time. 

At  present  the  student  needs  to  learn 
only  two  things :  first,  how  to  find  the  si- 
dereal time  at  Greenwich  corresponding 
to  any  given  hour  of  mean  time  there,  and 
secondly,  how  to  find  the  sidereal  time 
corresponding  to  any  given  hour  at  his 
own  meridian.  It  is  obvious  that  if  you 
can  find  the  former,  you  can  easily  get  the 
latter  by  applying  the  longitude  of  your 
meridian  (converted  into  time). 

A  sidereal  day  measures  in  mean  time — 
that  is,  by  a  chronometer  or  ordinary  clock 
— 23  hrs.,  56  min.,  04  sec.  In  other  words, 
every  hour,  minute,  and  second  in  a  side- 
real day  is  a  little  shorter  than  its  counter- 
part in  a  solar  day.  So,  in  turning  mean 
time  into  sidereal  time,  we  have  to  make 
some  allowances.  Table  VIII.,  Bowditch, 
gives  the  allowances  for  changing  sidereal 


127 


to  mean  time,  and  Table  IX.  for  changing 
mean  to  sidereal.  Similar  tables  are  to  be 
found  in  the  N.  A.,  back  part. 

The  N.  A.  will  give  you  the  sidereal  time 
at  Greenwich  noon  for  every  day  in  the 
year.  Hence  the  rule  for  converting  G. 
M.  T.  into  Greenwich  sidereal  time  (G.  S. 
T.)  is  this: 

Add  to  G.  M.  T.  the  G.  S.  T.  for  the  pre- 
ceding noon,  and  the  allowances  given  in 
Table  IX.  for  the  number  of  hours,  min- 
utes, and  seconds  in  the  G.  M.  T.  If  the 
sum  is  more  than  24  hours,  subtract  24 
hours  from  it,  because  at  the  end  of  24 
hours  Sid.  T.  begins  over  again. 

Example:  Required  G.S.T.,  Nov.  2, 1895, 
when  the  G.  M.  T.  by  chronom.  (corrected) 
was  7  hrs.,  25  min.,  15  sec. 

G.  M.  T 7  h.  25  m.  155. 

Sid.  T.  at  G.  at  preceding  noon. .  14  h.  4601.     1.98. 

From  table  7  hrs.  25  m.* . im.  13.13. 

Sid.  T.  at  G 22  h.  12  m.  30.0  s. 

*  The  i£  seconds  of  G.  M.  T.  are  disregarded  because  the  al- 
lowance is  only  .041**. 

Rule  for  finding  S.  T.  at  ship  or  R.  A. 
M.,  when  longitude  is  known :  Find  the 
mean  time  at  ship  by  applying  the  longi- 
tude to  the  G.  M.  T.  as  previously  explained. 


128 


Add  to  mean  time  at  ship  the  G.  S.  T.  for 
the  preceding  noon  and  the  allowances  for 
the  G.  M.  T.  from  Table  VIII.  If  the  result 
is  over  24  hours,  subtract  24  hours  from  it. 
-  Example:  Required  the  S.  T.  at  ship  Aug. 
J9»  I^95»  when  the  G.  M.  T.  was  11  hrs.,  15 
min.,  20  sec.  P.M.  Long.  60°  15'  W. 

G.  M.  T  .............   ii  h.  ism.  203. 

Long.  W  ............     4h.  01  m.  oos. 

M.  T.  at  ship  ........     7  h.  14  m.  20  s. 


...          9h.  5°m.  ,o.3S. 

Allow,  for  nh.  ism.  i  m.  50.85.  ,     . 

-  (or  Rt.  Ascension 
Sid.  T.  at  ship  ........  17  h.  06  m.  31.13.  {    Of  Meridian. 


All  this  is  necessary  here,  because  in 
order  to  work  the  lat.  by  the  polestar 
you  must  use  the  R.  A.  M.  In  north  lati- 
tudes the  polestar  is  available  at  any 
hour  of  the  night.  This  is  because  it  ap- 
parently revolves  around  the  north  pole 
of  the  heavens  at  a  distance  of  only  i°  20', 
making  the  change  of  altitude  so  slow  that 
it  can  be  used  always.  Of  course  the  star 
does  not  revolve  around  the  pole  at  all. 
It  is  the  earth  that  revolves.  The  student 
will  remember  what  has  been  said  about 
hour  -angle.  Now  it  is  obvious  that  the 
H.  A.  of  Polaris  may  be  very  great  without 


129 


any  serious  change  in  the  altitude.     Let 
the  centre  of  the  circle  be  the  north  pole 
of  the  heavens,  and  the  circumference  the 
apparent  orbit  of  Po- 
laris.    At  D  and  B 
the  altitude  of  the 
star  equals  the  alti- 
tude  of  the    pole, 
which  equals  the  lat. 
For  the  north   pole, 
being   90°   from   the 
equator,  will  be  in  the 
horizon  of  an  observ- 
er at  the  equator.    If 

you  go  10°  north  of  the  equator,  your 
northerly  horizon  will  drop  by  10°,  and 
hence  the  pole  will  be  10°  high,  and  so 
on  up  to  90°,  when  the  pole  would  be  over- 
head, or  90°  high.  With  the  polestar  at 
A  you  would  have  to  subtract  i°  20'  from 
its  altitude  to  get  the  altitude  of  the  pole, 
which  equals  the  lat. ;  at  C  you  would 
have  to  add  i°  20'.  Now  as  the  R.  A.  of 
M.  advances  from  o  to  24  hours  in  exactly 
the  same  time  as  the  polestar  appears  to 
revolve  around  the  pole,  the  astronomers 
have  made  a  table  for  us  by  which  we  can 
make  the  proper  addition  or  subtraction 


130 


to  the  altitude  of  Polaris  at  any  hour. 
What  you  have  to  do  is  to  find  the  H. 
A.  of  Polaris,  and  in  order  to  do  that 
you  must  first  get  the  S.  T.  at  ship.  Hence 
this  is  the  rule : 

Take  the  alt.  and  note  the  chronom. 
time  at  instant  of  observation.  Correct  the 
alt.  as  usual.  Find  the  sidereal  time  at 
ship  as  already  explained.  If  it  is  less 
than  i  hr.,  20  min.,  subtract  it  from  i  hr., 
20  min. ;  if  it  is  between  i  hr.,  20  min.,  and 
13  hrs.,  20  min.,  subtract  i  hr.,  20  min.  from 
it ;  if  it  is  greater  than  13  hrs.,  20  min.,  sub- 
tract it  from  25  hrs.,  20  min.  The  remain- 
der in  each  case  is  the  H.  A.  of  Polaris. 
Enter  Table  IV.,  on  the  last  page  of  the 
N.  A.,  with  the  H.  A.,  and  apply  the  correc- 
tion there  given  as  directed,  either  adding 
it  to  or  subtracting  it  from  the  corrected 
alt.  The  result  will  be  the  lat. 

Example:  At  sea,  Dec.  20,  1895.  Long. 
45°  1 5'  W. ;  obs.  alt.  of  Polaris,  40°  27'  oo" ; 
no  I.  E. ;  H.  of  E.,  20  ft. ;  G.  M.  T.,  1 1  hrs., 
30  min.,  oo  sec.  P.M.  (See  table  on  next 
page.) 

The  chief  difficulty  in  using  Polaris,  the 
student  will  find,  is  getting  the  altitude. 
The  star  is  very  small,  and  the  northern 


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part  of  the  sea  horizon  not  well  illumi- 
nated ;  but  it  can  be  done  after  practice, 
and  the  star  is  always  useful  as  a  check  on 
other  observations. 

It  is  now  possible  to  explain  how  to  work 
a  $'  and  $"  with  a  star  or  planet.  You 
must  find  the  hour-angle  of  the  star,  and 
that  is  always  the  difference  between  the 
R.  A.  of  the  star  and  the  R.  A.  of  your  me- 
ridian. You  will  understand  this  at  once 
if  you  have  fully  comprehended  what  R.  A. 
is.  And  you  will  also  understand  that  if 
the  star's  R.  A.  is  less  than  yours,  its  H.  A. 
is  west ;  and  if  it  is  greater  than  yours,  the 
H.  A.  is  east.  Always  subtract  the  less 
from  the  greater,  and  mark  the  H.  A.  east 
or  west  according  to  this  rule.  You  will 
need  this  point  again  in  star  time  azimuths, 
to  be  explained  presently. 

How  to  find  the  R.  A.  M.  has  already  been 
explained.  The  star's  R .  A.  is  got  from  the 
star  table  in  the  N.  A.  Having  the  H.  A., 
proceed  as  in  a  <£'  and  <£"  sight  of  the  sun. 

Example:  At  sea,  June  6,  1880.  Obs.  alt. 
of  star  Altair,  50°  17'  oo"  ;  no  I.  E. ;  H.of  E., 
22  ft.,  G.  M.  T.,4  hrs.,  38  min.,  09  sec.A.M. 
=  16  hrs.,  38  min.,  09  sec.,  astronom.time. 
Long.  23°  22'  W.  Required  lat.  of  ship. 


G.  M.  T  ...........   16  h.  38  m.  09  s.    Obs.  alt.  50°  17'  oo" 

Long.  W    ........       i  h.  33m.  405.    Cor  .  .  .  .  _  s'  *$" 

M.  T.  at  ship  ......  15  h.  04  m.  295.    T.  C.  A.  50°  n'  45" 


2m.  445. 


AHow^o^aM.'x. 

R.  A.  M 20  h.  04  m.  22  s. 

R.  A.  Altair 19  h.  44m.  593. 

Altair's  H.  A 19  m.  23  s.  =  4°  50'  45" 

H.  A 4°  50'  45"        sec...  .00156 

Dec .  8°  35' oo"       tang.. 9.17880       cosec...  .82609 

T.  C.  A.. 50°  xz'  45" sin 9.88552 

0" 8°  37' oo"       tang.  .9.18036        sin 9-17558 

0' 39°  32'  oo" cosine.  .9.88719 

Lat 48°  09'  oo"  N. 

The  above  example  is  taken  from  Lecky, 
who  works  it  by  the  Norie  method,  and 
gets  48°  o8f '  N.  as  his  latitude. 


COMPASS  ERROR   BY  AZIMUTHS 

It  is  possible  now  to  give  the  student 
further  directions  about  finding  the  com- 
pass error  by  azimuths.  The  method  was 
introduced  under  the  head  of  "  How  to 
Find  the  Deviation."  The  student  will  see 
now  that  in  employing  the  sun  what  he 
first  requires  is  the  sun's  H.  A.  Hence,  in 
taking  an  azimuth  by  the  sun,  the  longi- 
tude being  known,  proceed  thus : 


'34 


Note  the  time  of  the  azimuth  by  the 
chronom.  Correct  for  rate.  The  result  is 
G.  M.  T.  Convert  it  into  G.  App.  T.  by  ap- 
plying the  corrected  equation.  Convert 
G.  A.  T.  into  A.  T.  at  ship  by  applying  the 
longitude  in  time,  subtracting  it  when  west, 
adding  it  when  east.  The  result  is  the  A. 
T.  at  ship  or  local  H.  A.  of  the  sun.  En- 
ter the  azimuth  tables  with  this  and  the 
corrected  dec.  to  get  the  sun's  true  bear- 
ing. 

To  take  an  azimuth  by  the  moon,  a  planet, 
or  a  star. — Note  the  time  by  chronom. 
Apply  long,  to  get  M.  T.  at  ship.  Proceed 
to  find  the  H.  A.  of  the  celestial  body  as 
already  directed.  With  this  H.  A.  and  the 
dec.  get  the  true  bearing  from  the  azimuth 
tables. 


LONGITUDE  BY  CHRONOMETER  (OR  TIME) 
SIGHT 

The  foregoing  methods  of  obtaining  the 
lat.  by  observation  are  all  that  are  of  prac- 
tical value  at  sea.  The  double -altitudes 
method  is  available  in  no  instances  where 
Sumner's  problem  (yet  to  come)  is  not  bet- 


135 


ter,  and  Lecky's  ex-meridians  below  the 
pole  are  very  rarely  of  value.  Hence  we 
now  come  to  the  matter  of  longitude. 

Since  the  sun  revolves  (apparently) 
around  the  earth  once  in  24  hours,  passing 
through  15°  of  long,  every  hour,  if  we  can 
ascertain  how  many  hours  and  minutes 
east  or  west  of  Greenwich  the  sun  is,  and 
how  many  hours  and  minutes  east  or  west 
of  the  sun  we  are,  we  shall  know  our  long. 
When  the  long,  is  not  known,  then  the 
problem  is  to  find  the  local  H.  A.  of  the 
sun. 

The  H.  A.  from  Greenwich  we  carry 
with  us  in  the  shape  of  the  chronom., 
which  tells  us  G.  M.  T.,  and  that,  of  course, 
is  simply  the  H.  A.  of  the  sun  there.  If 
we  find  the  H.  A.  here — at  our  meridian — 
the  difference  between  the  two  will  be  the 
number  of  hours,  minutes,  and  seconds  we 
are  east  or  west  of  the  Greenwich  merid- 
ian, and  this  quantity  is,  as  we  have  seen, 
convertible  into  the  degrees,  minutes,  and 
seconds  of  longitude. 

The  computation  of  the  H.  A.  of  the  sun 
is  a  complicated  problem  in  spherical  trig- 
onometry; but  the  navigator  has  only  to 
know  how  to  use  the  tables  prepared  by 


'3* 


the  astronomers  and  to  employ  simple 
arithmetic. 

The  necessary  data  are  the  T.  C.  A.,  the 
polar  distance,  and  the  latitude.  At  the 
instant  of  getting  the  altitude  with  the  sex- 
tant, note  the  chronom.  time  accurately  and 
correct  it  for  rate.  Make  the  corrections  for 
dec.  and  equation  of  time  according  to  the 
G.  M.  T.  Then  convert  G.  M.  T.  into  G.  App. 
T.  by  applying  the  corrected  equation  as 
directed  by  the  N.  A.  You  need  G.  App. 
T.  because  from  your  observation  of  the 
sun  you  get  L.  App.  T.  If  you  prefer,  you 
can  wait  till  you  have  computed  that,  and 
then  convert  it  into  L.  M.  T.  so  as  to  com- 
pare it  with  G.  M.  T.  The  first  way  is  a 
little  more  convenient. 

Take  out  the  dec.  for  Greenwich  noon, 
and  correct  it  for  hourly  change  just  as  in 
a  lat.  observation.  If  you  are  in  N.  lat. 
and  the  dec.  is  N.,  or  in  S.  lat.  and  the  dec. 
is  S.,  subtract  the  corrected  dec.  from  90° 
to  get  the  polar  distance.  If  you  are  in 
N.  lat.  and  dec.  is  S.,  or  in  S.  lat.  and 
dec.  is  N.,  add  dec.  to  90°  to  get  P.  D. 
The  rule  for  the  rest  of  the  operation  is 
this : 

Add  together  the  P.  D.,  the  lat.,  and  the 


*37 


T.  C.  A.  Divide  the  sum  by  2,  and  call  the 
quotient  the  half-sum.  From  the  half-sum 
subtract  the  T.  C.  A.,  and  call  the  answer 
the  difference.  Now  add  the  cosecant  of 
the  P.  D.,  the  secant  of  the  lat.,  the  cosine 
of  the  half-sum,  and  the  sine  of  the  differ- 
ence obtained  from  Table  XLIV.  If  the 
index  of  the  sum  is  more  than  9  (say  18), 
set  it  down  so.  Divide  this  sum  by  2. 
The  quotient  is  the  sine  of  apparent  time 
at  the  ship,  which  you  are  to  take  out  of 
the  A.M.  column  of  Table  XLIV.  if  the  ob- 
servation was  an  A.M.  one,  from  the  P.M. 
column  if  P.M.  The  difference  between 
the  App.  T.  at  ship  and  G.  App.  T.  is  the 
long,  of  the  ship  in  time,  which  turn  into 
degrees,  minutes,  and  seconds.  If  G.  App. 
T.  is  greater  than  App.  T.  at  ship,  long,  is 
west ;  if  less,  long,  is  east.  Or,  in  the  mem- 
orizing rhyme : 

Greenwich  time  best, 
Longitude  west  ; 
Greenwich  time  least, 
Longitude  east. 

Example  i :  At  sea,  Oct.  i,  1895.  A.M.  obs. 
alt.  Q  17°  is'oo";  G.  M.T.,  u  hrs,,  30  min. 
A.M.  ;  lat.  40°  30'  N. ;  H.  of  E.,  1 5  ft.;  I.  £.—3'. 


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Example  2:  At  sea,  Oct.  i,  1895.  P.M. 
obs.  alt.  O  20°  15'  oo";  G.  M.  T.,  i  hr.,  15 
min.  P.M.,  lat.  40°  30'  S. ;  H.  of  E.,  15  ft. 
(See  table  on  page  140.) 

The  student  must  now  learn  how  to  use 
the  proportional  parts  of  the  columns  A, 
B,  and  C,  in  Table  XLIV.  In  the  last  ex- 
ample, for  instance,  the  sine  of  App.  T., 
9.73435,  is  found  exactly  as  it  stands  in  the 
column  of  sines,  and  opposite  it,  in  the 
P.M.  column,  are  the  hours,  minutes,  and 
seconds  taken  out.  But  suppose  the  sine 
had  been  9.73421.  This  will  not  be  found, 
for  the  next  sine  smaller  than  9.73435  is 
9.73416.  In  working  long,  you  must  be 
careful  about  the  seconds,  because  4  sec. 
of  time  =  i'  of  long.  Hence  we  proceed 
thus :  Take  the  difference  between  the 
sine  of  App.  T.  and  the  sine  nearest  to  it 
in  the  table.  Apply  the  difference  in  the 
little  table  at  the  bottom  of  the  page  op- 
posite the  letter  of  the  column  from  which 
the  sine  was  taken.  Above  this  will  be 
found  the  number  of  seconds  which  must 
be  added  to  or  subtracted  from  the  time 
given  in  the  A.M.  or  P.M.  column.  If  the 
sine  of  A.  T.  is  larger  than  the  sine  in  the 
table,  add  the  difference  obtained  from  the 


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little  table  to  the  given  time ;  otherwise 
subtract  it. 

Example:  Obtained  sine  of  App.  T.  at 
ship,  9.73421.  Difference  between  this  and 
nearest  sine  in  table,  5.  Nearest  sine  be- 
ing found  in  col.  A,  apply  5  in  proportion- 
al parts  of  col.  A,  at  bottom  of  page. 
Above  5  find  2  sec.  Add  2  sec.  to  the 
time  given  for  sine  9.73416,  and  you  get 
the  correct  time  for  sine  9.73421,  which  is 
(P.M.)  4  hrs.,  22  min.,  42  sec. 


REMARKS  ON   LONGITUDE 

As  the  lat.  is  best  obtained  when  the 
sun  bears  due  north  or  south,  so  the  long, 
is  most  accurately  found  with  the  sun  due 
east  or  west.  This,  however,  you  can 
rarely  get,  for  to  have  the  sun  due  east  or 
west  of  you,  your  lat.  and  the  dec.  of  the 
sun  must  be  the  same.  If  the  sun  rose 
due  east  every  day  and  travelled  across 
the  sky  due  west,  long,  would  be  got  just 
like  lat.  You  know  that  it  is  just  90°  from 
the  horizon  to  the  zenith,  and  you  know 
that  90°  is  just  a  quarter  of  a  circle.  Now 
suppose  the  sun  to  be  due  east  of  you 


X42 


when  its  alt.  was  70°.  By  subtracting  the 
alt.  from  90°  you  would  know  that  the  sun 
had  just  20°  to  pass  through  before  cross- 
ing your  meridian.  In  other  words,  its  H. 
A.  would  be  20°,  which  =  i  hr.,  20  min., 
and  hence  your  App.  T.  would  be  10  hrs., 
40  min.  A.M. 

When  the  sun  is  due  east  or  west  of  you 
it  is  said  to  be  in  the  prime  vertical  (P.  V.). 
But  as  the  sun's  dec.  is  almost  invariably 
more  or  less  than  your  lat.,  your  observa- 
tions for  long,  are  nearly  all  ex-prime  ver- 
tical. The  farther  away  from  the  prime 
vertical  the  sun  is,  the  more  accurately 
you  need  to  know  your  lat.,  while  if  the 
sun  is  on  the  P.  V.,  an  error  of  half  a  de- 
gree in  the  lat.  will  make  no  serious  dif- 
ference in  the  long.  How  valuable,  then, 
are  the  stars,  from  which  you  can  almost 
always  select  one  which  is  nearly  on  the 
P.  V.,  if  not  exactly  so.  In  the  North  At- 
lantic in  winter,  when  the  sun  is  20  odd 
degrees  below  the  equator,  far  away  from 
the  P.  V.,  the  sky  is  full  of  bright  stars 
whose  declinations  bring  them  well  up 
towards  the  P.  V. 

The  employment  of  stars  in  long,  will 
be  explained  in  the  proper  place.  The 


point  to  be  urged  here  is  this  :  Try  to  get 
the  sun  when  it  bears  most  nearly  east  or 
west  of  you.  To  ascertain  at  what  time  it 
will  be  so  enter  the  azimuth  tables  wkh 
your  lat.  and  the  sun's  dec.  The  tables 
give  the  true  bearing  of  the  sun  for  every 
4  minutes  of  the  day,  and  you  can  select 
the  bearing  which  is  nearest  to  E.  or  W., 
and  take  your  observation  at  the  time  in- 
dicated. Do  not  fall  into  the  common  hab- 
it of  the  merchant  marine  of  always  taking 
the  long,  at  the  same  hour.  Select  the  right 
time  and  get  good  results. 


LONGITUDE   BY  SUNRISE  AND   SUNSET 
SIGHTS 

The  chronometer  sight  is  the  standard 
method.  Sometimes,  however,  it  is  cloudy 
all  day  and  the  sun  appears  just  at  setting. 
The  rule  for  sunrise  or  sunset  sights  is  as 
follows : 

Note  the  chronom.  time  when  the  sun's 
upper  or  lower  limb  touches  the  horizon. 
Correct  the  chronom.  for  rate.  Correct  the 
dec.  as  usual,  and  find  the  polar  distance. 
Add  the  lat.  and  P.  D.,  and  from  the  sum 


subtract  21'  if  the  lower  limb  was  observed, 
or  53'  if  the  upper  limb.  Divide  the  answer 
by  2  to  obtain  the  "  half-sum,"  and  add  the 
21  or  53  previously  subtracted  to  obtain  the 
"diff."  Then  proceed  as  in  a  chronom. 
sight,  adding  the  cosec.  of  the  P.  D.,  sec. 
of  the  lat.,  cosine  of  the  half-sum,  and  sine 
of  the  diff.,  and  taking  out  App.  T.  at  ship 
to  compare  with  App.  T.  at  Greenwich. 

Example :  Aug.  16,  1895.  Lat.  48°  10'  N. 
Lower  limb  O  touched  horizon  at  8  hrs.,  30 
min.,  15  sec.,  by  chronom.,  slow  of  G.  M.  T. 
i  min.,  15  sec.  (See  table  on  next  page.) 

This  method  is  not  often  of  value,  and 
should  be  employed  only  when  there  is  no 
chance  of  getting  a  chronometer  sight  of 
the  sun  or  some  other  celestial  body. 


CHRONOMETER  SIGHT  OF  A  STAR 

The  problem  is  to  find  the  sidereal  time 
at  the  ship,  and  compare  it  with  the  side- 
real time  at  Greenwich.  As  there  are  24 
hours  in  a  sidereal  day,  each  hour  equals 
15°  of  longitude,  as  in  solar  time.  Hence 
long,  can  be  obtained  as  well  from  sidereal 
as  from  solar  time.  The  rule  is  as  follows: 


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Take  the  altitude  and  note  the  chronom. 
time  as  usual.  Convert  G.  M.  T.  into  G. 
Sid.  T.  as  already  explained.  Find  the 
hour-angle  of  the  star  by  the  use  of  the 
P.  D.,  lat.,  and  alt.  in  exactly  the  same  way 
as  for  the  sun — only  always  take  the  H.  A. 
of  a  star,  planet,  or  the  moon  from  the 
P.M.  col.  of  Table  XLIV.  If  the  H.  A.  is 
east  (which  you  can  tell  by  the  bearing  of 
the  star),  subtract  it  from  the  star's  R.  A. ; 
if  H.  A.  is  west,  add  it  to  star's  R.  A.  The 
result  is  the  R.  A.  of  your  meridian,  or  si- 
dereal time  at  ship,  and  the  long,  is  the  dif- 
ference between  it  and  the  G.  Sid.  T.  The 
rule  is  the  same  for  the  moon  and  the 
planets. 

Example :  Dec.  i,  1895.  Obs.  alt.  of  Sir- 
ius,  20°  10' oo".  Chronom.  11  hrs.,  15  min., 

00  sec.  P.M.     Chronom.  slow  of  G.  M.  T. 

1  min.,  26  sec. ;  no  I.  E. ;  H.  of  E.,  20  ft. ; 
lat.  38°  58'  N.    (See  table  on  next  page.) 

It  is  a  good  practice  aboard  ships  pro- 
vided with  plenty  of  officers  or  well  -  in- 
structed quartermasters,  to  make  use  of 
any  hour-angle  obtained  from  a  chronom- 
eter sight  for  an  azimuth.  This  is  to  be 
done  by  observing  the  compass  bearing  of 
the  celestial  body  at  the  instant  of  taking 


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the  altitude,  and  then  getting  the  true 
bearing  from  the  tables.  In  case  of  work- 
ing with  a  star  whose  declination  exceeds 
the  23°  given  in  the  table,  the  true  bearing 
may  be  computed  by  the  altitude-azimuth 
problem,  in  conjunction  with  a  chronom- 
eter'sight.  The  rule  for  this  is  as  follows : 

Add  together  the  P.  D.,  lat.,  and  the  T.  C. 
A.  Divide  the  sum  by  2  and  call  the  an- 
swer half-sum ;  take  the  difference  between 
the  half-sum  and  the  P.  D.,  and  call  the  an- 
swer diff. 

Add  together  the  secant  of  the  lat.,  the 
secant  of  the  alt.,  the  cosine  of  the  half- 
sum,  and  the  cosine  of  the  diff.  Half  their 
sum  is  the  cosine  of  half  the  angle  of  the 
true  bearing,  which  must  be  doubled  and 
reckoned  from  north  in  north  lat.,  and 
from  south  in  south  lat. 

Example :  Take  the  time  sight  of  Sirius, 
just  used,  and  work  it  for  the  azimuth. 

P.D..io6°  34-00" 

Lat...  38°  58'  oo"  sec...  .10929 

Alt...   20°  Q3/  oo"  sec...  .02715 

2 )  165°  35'  20" 

#-sum  82°  47'  40"  cos..  9.09807 
Piff. ..  23°  46'  20"  cos..  9.96151 
2  )  19.19602 
cos..  9.59801=66°  39' 


149 


The  beauty  of  this  process  is  that  the 
additional  amount  of  work  is  so  small. 
You  already  have  the  secant  of  the  lat. 
and  the  cosine  of  the  half -sum,  and  it 
takes  only  a  few  extra  seconds  to  get  the 
other  two  logarithms.  You  need  never  be 
in  doubt  as  to  which  angle  to  select  from 
Table  XLIV.  (which  has  two  at  the  top  and 
two  at  the  bottom  of  the  page),  because 
the  bearing  must  be  less  than  180°,  and  for 
a  first-class  longitude  sight  it  ought  to  be 
as  close  to  90°  as  possible. 


SUMNER'S  METHOD 

We  come  now  to  the  most  valuable  of 
all  known  methods  of  finding  a  ship's  posi- 
tion at  sea.  Two  or  three  makeshift 
methods  of  finding  the  longitude  might 
have  been  explained ;  but  this  is  a  purely 
elementary  and  practical  work,  and  it  is 
deemed  useless  to  introduce  infrequent 
workings  when  by  Sumner's  method  we 
can  find,  at  almost  any  hour  of  the  day 
or  night,  the  latitude,  longitude,  and  error 
of  the  compass  by  simply  working  two 
chronometer  sights.  Furthermore,  we  can 


'50 


get  a  great  deal  of  information  from  one 
sight. 

Sumner's  method  is  based  on  certain 
fundamental  truths  of  navigation,  which 
I  shall  now  endeavor  to  explain,  following 
pretty  closely  the  admirable  explanation 
of  Captain  Lecky. 

Wherever  the  sun  is,  it  must  be  perpen- 
dicularly above  some  spot  on  the  surface 
of  the  earth.  Sup- 
pose the  sun  to  be 
immediately  above 
the  centre  of  the  cir- 
cle, S.  Then  if  a 
\C  man  at  A  takes  an 
altitude,  he  will  get 
precisely  the  same 
one  as  men  at  B,  C, 
D,  and  E,  because 
they  are  all  at  equal 

distances  from  the  sun,  and  hence  on  the 
circumference  of  a  circle  whose  centre  is 
S.  Conversely,  if  several  observers  situ- 
ated at  different  parts  of  the  earth's  sur- 
face take  simultaneous  altitudes,  and  these 
altitudes  are  all  the  same,  then  these  ob- 
servers must  all  be  on  the  circumference 
of  a  circle,  and  only  one  circle.  If  you 


moved  one  observer  to  the  circumference 
of  a  larger  circle,  for  instance,  he  would  be 


farther  away  from 
get  a  smaller  alti- 

Now  such  a  cir- 
of  the  earth  would 
large  that  a  small 
ference,  say  20  or 
practically  a 
pose  D  to  be  the 
the  sun  is  vertical, 
of  the  circumfer- 
drawn  around  this 
you  were  at  C,  and 
the  sun  you  work- 
tion.  You  would 
little  arc  AB,  which 
p  u  r poses  is  a 
right  angles  to  the 
sun  from  the  point 
discern  by  simply 

Suppose  now  we 


the  sun  and  would 
tude. 

cle  on  the  surface 
be  very  large  —  so 
arc  of  its  circum- 
30  miles,  would  be 
straight  line.  Sup- 
point  over  which 
and  HP  to  be  part 
ence  of  a  circle 
point.  Suppose 
from  an  altitude  of 
ed  out  your  posi- 
find  yourself  on  the 
to  all  intents  and 
straight  line  at 
true  bearing  of  the 

C,  as  you  may 
.  g     looking  at  it. 

continue   the 


circle  around  D.     Place  an  observer  at  J, 


'52 


and  let  him  take  an  altitude  of  the  sun. 
He  will  be  on  the  circumference  of  the  same 
circle,  but  on  the  small  arc  QN,  which  is 
again  practically  a  straight  line  and  at 
right  angles  to  the  true  bearing  of  the  sun. 
At  S  he  would  find  himself  on  the  arc  RT 


\ 


— again  a  small  straight  line  at  right 
angles  to  the  bearing  of  the  sun. 

If  you  draw  any  other  circle,  and 
mark  points  of  observation,  you  will 
get  similar  results. 


Hence :  Any  person  taking  an  altitude 
of  a  celestial  body  must  be,  for  all  practi- 
cal purposes,  on  a  straight  line  which  is  at 
right  angles  to  the  true  bearing  of  the 
body  observed. 

Such  a  line  is  called  a  Sumner  line,  or  a 
line  of  position. 

It  must  now  be  perfectly  clear  to  the 
student  that  if  the  sun  bears  due  north  or 
south  of  the  observer,  the  resulting  line  of 
position  must  run  east  and  west ;  or,  in 
other  words,  it  is  a  parallel  of  lat.  And 
that  explains  why  a  meridian  observation 
gives  the  most  accurate  lat. 

Again,  if  the  sun  bears  due  east  or  west 
the  resulting  line  of  position  must  run 
north  and  south ;  or,  in  other  words,  it  is 
a  meridian  of  longitude.  And  that  explains 
why  a  prime  vertical  observation  gives  the 
most  accurate  longitude.  The  observer  at 
J  might  be  well  over  towards  Q  or  N — in 
other  words,  mistaken  considerably  as  to 
his  latitude — but  he  would  get  his  longi- 
tude all  right. 

But  in  the  case  of  the  man  at  S,  the 
longitude  cannot  be  known  exactly  un- 
less the  lat.  is.  Transfer  the  line  to  a  chart. 
We  know  that  we  are  somewhere  on  that 


8o*           75°         70*          65 

C 

/ 

50" 
45* 
40* 

& 

/ 

** 

line  RT.  If  the  latitude  is  50°  N.,  we  must 
be  at  the  point  where  the  line  crosses  the 
5oth  parallel,  which 
is  at  B.  If  the  lat. 
is  55°,  we  must  be  at 
C.  This  shows  how 
necessary  the  lat.  is  in 
cases  where  the  ob- 
served body  does  not 
bear  east  or  west.  On 
the  other  hand,  if  you 
wished  to  get  your 
lat.  from  the  line  RT, 
you  would  have  to  know  your  long,  ac- 
curately. If  the  long,  was  70°  W.,  you 
would  know  you  were  at  C. 

Hence  we  get  this  operation  from  a  sin- 
gle Sumner  line:  Whenever  you  take  a 
chronometer  sight  of  the  sun,  or  any  other 
heavenly  body  from  the  H.  A.,  obtained 
in  the  computation,  get  the  true  bearing 
of  the  body  from  the  azimuth  tables,  or  by 
the  alt.-azimuth  problem.  Then,  through 
the  position  obtained,  draw  a  Sumner  line 
running  at  right  angles  to  the  true  bearing. 
You  are  absolutely  sure  to  be  somewhere 
on  that  line  at  the  instant  of  observation; 
you  cannot  possibly  be  on  any  other, 


'55 


Now  suppose  that  you  took  the  observa- 
tion at  8  A.M.,  and  that  you  were  not  quite 
sure  of  your  lat.  by  D.  R.  From  8  A.M.  till 
noon  the  ship  sails  60  miles  E.N.E.,  and 
then  you  get  a  meridian  alt.  and  are  sure 
of  your  lat.  Through  the  point  E,  the  8 


SUN 


A.M.  position,  draw  the  Sumner  line  AB, 
at  right  angles  to  the  sun's  true  bearing  at 
8  o'clock.  From  the  point  E  lay  off  on 
the  chart  60  miles  E.N.E.  on  the  line  EF. 
At  F,  the  extremity  of  EF,  rule  a  new 


i56 


Sumner  line,  exactly  parallel  to  the  old 
one.  At  the  point  G,  where  the  parallel  of 
your  noon  lat.  cuts  the  Sumner  line,  is  the 
position  of  the  ship  at  noon. 

The  old,  established  way  of  making  a 
noon  position  is  this  :  Take  your  morning 
sight  for  long.,  but  do  not  work  it  out. 
Take  your  noon  sight  for  lat.,  and  then  by 
D.  R.  compute  backward  to  the  correct  lat. 
at  the  time  of  the  morning  sight,  and  with 
this  lat.  work  out  the  longitude.  Then 
carry  the  longitude  up  to  noon  by  D.  R., 
and  thus  establish  the  lat.  and  long,  at  noon. 

The  method  by  a  Sumner  line  and  a  par- 
allel is  far  shorter  and  quite  as  accurate. 
By  it  you  have  found  that  you  are  on  small 
arcs  of  two  different  circles  at  the  same 
time.  You  can  be  only  at  their  point  of  in- 
tersection. And  that  is  the  whole  theory 
of  the  Sumner  method. 

The  old-fashioned  way  of  working  a 
Sumner  line  is  to  assume  two  latitudes, 
say  25'  or  30'  apart,  and  about  equally  dis- 
tant from  the  lat.  by  D.  R.,  work  out  the 
chronometer  sight  with  each,  lay  down  the 
two  different  positions  on  the  chart,  and 
rule  a  line  joining  them.  This  will  be  your 
Sumner  line.  But  why  do  all  that  when 


one  working-out  is  sufficient?  Any  posi- 
tion at  all  must  be  on  a  line  at  right  angles 
to  the  sun's  true  bearing,  and  that's  your 
Sumner  line. 

Suppose  you  are  approaching  a  coast  on 
which  there  is  a  high  mountain  visible  60 
miles  at  sea.  There  are  reefs  off  the  coast. 
You  are  uncertain  of  your  lat.  within  6  or 


158 


8  miles,  but  you  fear  you  will  reach  the 
neighborhood  of  the  reefs  before  soon. 

At  9.30  you  get  k  cnronom.  sight  and 
draw  the  Sumner  line  CD.  Put  the  ship 
on  that  line  and  sail  on  it.  At  10.45  you 
sight  the  mountain  bearing  N.  true.  Draw 
a  line  running  N.  and  S.  true  till  it  cuts 
your  line  of  bearing.  That  is  your  posi- 
tion. The  only  thing  in  the  world  that 
could  put  you  wrong  in  this  instance  would 
be  a  current,  and  you  must  guard  against 
that  by  using  the  lead  according  to  the 
method  of  sailing  along  a  chain  of  sound- 
ings already  explained. 

This  introduces  us  to  the  excellent  use 
of  a  single  Sumner  line  when  running  in 
with  the  land.  The  simplest  form  of  the 
operation  is  to  take  a  chronometer  sight 
and  get  a  line  of  bearing.  Suppose  you  are 
standing  in  towards  a  coast  which  you 
know  to  be  northwest  of  you.  Your  posi- 
tion is  not  quite  certain.  You  take  a  chro- 
nometer sight  and  get  a  position  from 
which  the  sun  bears  W.S.W.fW.  You 
rule  the  Sumner  line  AB  at  right  angles 
to  it,  running  N.-by-W.iW.  Continue  the 
line  till  it  meets  the  land  at  the  point  C 
Obviously  if  you  sail  on  the  Sumner  line 


heading  N.-by-W.^W.  true,  you  will  make 
the  point  C. 

Suppose  that  at  C  there  stood  a  well- 
known  light-house,  whose  light 
was  visible  18  miles  at  sea  in 
clear  weather.    When  that 
light  popped  into  view 
over    the    horizon, 
you    could    at    once 
verify    your    posi- 
tion by  taking  its 
bearing,  and  then 
sail  in  with  bold- 
ness— not  forget- 
ting to  use  the  lead. 

But   suppose    you    do   not 
wish    to   make   the    point    C, 
which    is  at   the  end  of   your 
Sumner   line.     Some    20  miles 
farther  up  the  coast  is  a  well- 
lighted  harbor,  and  you  wish  to 
make  that.     All  you  have  to  do  is 
to  draw  a  second  line  of  bearing, 
parallel  to  the  first 
and  ending  at  the 
point  you  wish  to 
make.      Measure 
the  distance  at 


right  angles  between  your  two  lines  ot 
bearing.  Sail  over  that  course  and  dis- 
tance. You  will  then  be  on  the  second 
line  of  bearing,  when  you  at  once  take  the 
course  N.-by-W.JW.  true,  of  the  first  line, 
and  you  are  bound  to  make  your  harbor. 


Let  us  see  how  this  will  work  in  practice. 
Suppose  it  to  be  late  in  the  afternoon  of  a 
cloudy  day  in  winter,  and  you  are  a  little 
anxious  because  you  have  had  no  sights 
for  longitude  since  3  o'clock  in  the  morn- 
ing. Just  before  sundown  the  sun  appears 
and  you  get  a  sunset  sight. 

Feb.  25,  1895.  Lat.  30°  15'  N.  The 
lower  limb  of  the  sun  touched  the  horizon 
at  9  hrs.,  32  min.,  15  sec.  by  chronom. 
Chronom.  fast  of  G.  M.  T.  3  min.,  15  sec. 
Required  a  line  of  bearing. 

G.  M.  T.-gh.  29  m.  oos.  P.M.  Hourly  diff.  dec.  55.8" 
Cor.  equ.  13  m.  10.8  s.  Time  after  noon.  _9>£ 
G.  A.  T.  .  .gh.  15  m.  49.25.  279 


Cor.  dec....  80  55'  29"  S. 

5° 
Cor.  dec..     8°  55'  29"$. 

90°  oo'  oo" 
P.  D  .....  98°  55'  29"  cosec.     .00528 

Lat  .......  30°  15'  oo"  sec.  ..     .06357 

Const  ----          21' 

2  )  129°  IO'  29" 

}£-sum...  64°  24'  44"  cos...  9.63531 

21' 
Diff  .....    64°  45'  44"  sin...  9-95645 

2  )  19.66061      h.  m.   s. 

9.83030  =  5    40  36  A.  T.  S. 
9    15   49  A.  T.  G. 

Long....  53°  48'  15"  W  =  3    35    »3 
By  Table  XXXIX.  true  bearing  of  sun  =  N.  100°  W., 
or  about  W.-by-S.     Sumner  line  will  run  N.-by-W. 
ix 


If,  now,  you  had  land  to  the  northward, 
your  Sumner  line  would  enable  you  to  set 
a  correct  course  to  make  it  at  the  proper 
place.  As  a  matter  of  fact  lat.  30°  15'  N. 
and  long.  41°  21'  W.  are  well  to  the  south- 
ward and  westward  of  the  Azores  ;  but  the 
principle  remains  the  same. 

If  so  much  can  be  done  with  a  single 
Sumner  line,  how  much  more  can  be  done 
with  two.  For  if  you  can  locate  your  ship 
on  two  Sumner  lines  at  once,  you  know 
that  she  can  be  on  but  one  place  on  either, 
and  that  is  the  point  of  intersection  of  both. 

There  are  two  ways  of  getting  two  Sum- 
ner lines,  one  by  two  successive  observa- 
tions of  the  same  body,  and  the  other  by 
simultaneous  observations  of  two  bodies. 
The  latter  is,  of  course,  preferable,  but  it  is 
not  available  in  the  daytime. 

As  applied  to  the  sun  the  method  is  as 
follows :  Take  an  observation,  work  it  out 
with  your  lat.  by  D.  R.,  and  draw  a  Sum- 
ner line  as  already  explained.  Now  wait 
till  the  sun's  bearing  alters  at  least  2 
points.  Take  another  observation  and 
draw  another  Sumner  line.  It  is  obvious 
that  it  will  make  an  angle  of  at  least  2 
points  with  the  first  one.  The  point  of 


intersection  of  the  two  lines  is  the  position 
of  the  ship. 

This,  however,  supposes  the  ship  to  be 
standing  still.  In  practice  she  is  making 
progress,  and  it  becomes  necessary  to  car- 
ry forward  the  first  Sumner  line  to  the 
place  of  the  second  observation.  This  is 
done  by  a  process  similar  to  that  given  for 
plotting  a  noon  position. 

Having  taken  your  first  sight  and  drawn 
your  Sumner  line,  from  any  point  on  this 
line  lay  off  the  course  and  distance  made 
up  to  the  time  of  taking  the  second  sight 
and  drawing  the  second  Sumner  line.  At 
the  extremity  of  the  course -line  draw 
a  third  line  parallel  to  the  first  Sumner 
line,  and  prolong  it  till  it  cuts  the  second 
Sumner  line.  The  intersection  of  this  par- 
allel with  the  second  Sumner  line  will  be 
the  position  of  the  ship  at  the  time  of  the 
second  observation.  For  instance,  suppose 
that  in  the  diagram  your  first  observation 
gave  you  the  line  of  bearing  AA,  and  your 
second  the  line  BB.  Between  the  two  sights 
the  ship  sailed  E.N.E.  40  miles.  You  lay 
off  E.N.E.  40  miles  from  any  point  on  AA, 
and  draw  CC  parallel  to  AA.  The  intersec- 
tion of  CC  and  BB  at  S  is  the  position  of  the 


•64 


ship  at  the  time  of  the  second  observa- 
tion. 


At  night,  however,  you  might  get  two 
stars,  one  east  and  the  other  west  of  you, 
and  take  observations  of  both  so  closely 
together  as  to  be  practically  simultaneous. 
Then  your  easterly  star  would  give  the 
line  AA  and  the  westerly  star  the  line 
BB,  and  you  would  be  at  S  (as  on  p.  165). 


8 


EXAMPLE  OF  SUMNER  S   METHOD   WITH 

THE  SUN 

At  sea,  June  i,  1895.  Obs.  alt.  O  33° 
50'  oo" ;  G.  M.  T.,  8  hrs.,  55  min.,  oo  sec. 
P.M.  ;  H.  of  E.,  20  ft. ;  no  I.  E. ;  lat.  40* 
17'  N.  (See  table  on  page  166.) 

Two  hours  later  took  another  sight, 
which  gave  a  corrected  alt.  of  11°  50';  G. 
M.  T.,  10  hrs.,  55  min.  Ship  in  the  mean- 
time made  1 2  m.  N.-by-W.f  W.  (See  table 
on  page  167.) 

From  azimuth  tables  true  bearing  of 
sun  N.  69°  48'  W.  or  W.N.W.JW.  Sumner 
line,  N.-by-E.f  E. 

I  have  selected  these  positions  because, 
owing  to  the  high  declination  of  the  sun, 
its  bearing  alters  only  a  point  and  a  half 
in  the  two  hours,  and  hence  makes  a  bad 
"  cut,"  as  it  is  called,  for  the  two  Sumner 
lines.  Yet  see  how  plain  it  all  is  when 


1 66 


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drawn  to  a  scale  even  smaller  than  that  of 
a  chart. 

It  appears  from  this  that  the  latitude  by 
D.  R.  was  in  error  8'  southerly.  Yet,  ow- 
ing to  the  westerly  bearing  of  the  sun,  the 
error  in  the  longitude  amounted  to  only 
4/.  Captain  Lecky  gives  a  table  showing 
the  error  in  longitude  corresponding  to  an 


'69 

error  of  i'  in  latitude  at  different  bearings 
of  the  sun,  and  another  showing  the  error 
for  i'  of  altitude.  They  are  most  instruc- 
tive. For  the  bearing  of  the  sun  in  our 
second  observation  above  he  gives  an  error 
of  .47  of  a  minute  of  long,  for  every  error 
of  i'  in  lat.  For  8'  lat.  this  would  make 
3.76'  of  long,  which  conies  pretty  near  what 
we  get  from  simply  laying  off  the  lines  with 
a  protractor  and  scale  of  equal  parts.  At 
sea,  working  on  a  chart,  we  should  use  the 
parallel  rules  (or  protractor)  and  dividers. 

The  true  bearing  of  the  sun,  required  for 
the  Sumner  line,  can  always  be  used  to  get 
the  deviation.  Thus  by  this  fine  method 
we  obtain  from  two  sights  the  latitude, 
longitude,  and  error  of  compass. 

In  the  above  illustration  the  first  bearing 
of  the  sun  is  worked  out  by  the  altitude- 
azimuth  rule  simply  for  illustration ;  in 
practice  it  would  be  taken,  as  the  second 
is,  from  the  azimuth  tables. 

Now  let  us  see  what  can  be  done  with 
two  well-chosen  stars.  To  make  a  good 
choice,  get  two  stars  whose  bearings  from 
the  ship  are  as  nearly  at  right  angles  a? 
possible.  This  will  bring  the  intersecting 
Sumner  lines  nearly  at  right  angles  and 


make  the  position  clearer.  This  compu- 
tation, you  see,  is  nothing  more^  or  less 
than  astronomical  cross-bearings. 


EXAMPLE    OF   SUMNER    LINES    WITH    TWO 
STARS 

At  sea,  Jan.  i,  1895.  Obs.  alt.  Procyon  32° 
44'  oo"  E.,  and  a  Arietis  58°  21'  oo"  W. ;  lat. 
by  D.  R.  39°  45'  N. ;  H.  of  E.,  20  ft. ;  no  I. 
E. ;  G.  M.  T.,  first  observation,  12  hrs.,  01 
min.  P.M.;  second  obs.,  12  hrs.,  02  min.,  10 
sec.  P.M.  Required  position  of  ship  by 
Sumner's  method. 

G.  M.  T i2h.  oim.  oos.        Dec.  Procyon 5°  29'  37"  N. 


Allowance  

i  m.  585. 

30  h.  46m.  305. 
24  h. 

Obs.  alt.  Procyon...  32*  44'  oo" 

G.  Sid.  T  

6h.  46m.  30  s. 

Refr  **    3?'?8'' 

T.  C.  A  «*  a*  10" 

P.  D 84"  30'  23"    cosec. 

'Lat 39°  45'  oo"    sec   . . 

T.  C.  A..  32°  38' 19" 


%-sum...  78°  26'  51"    cos 9.30151 

Diff. 45°  48*  32"    sin 9-85559 

2)19.27326 

9.63663—  3h.  asm.  20 s.  H.  A.  East. 

True  bearing  of  #•  N.  113*  E.  /h.  33m.  48$.  R.A.Procyon 

Sumner  line  N.  23'  H.  or  S.  23'  W.  4h.  o8m.  zSs.Sid.T.atship 

6h.  46m.  30 s.Sid.  T.  at  ( .. 
Long... 39*  30*  30"  W.=  ah.  38 in.  02 s. 


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Plotted  according  to  a  scale  of  miles 
and  with  a  protractor,  the  Sumner  lines 
cut  as  below,  making  the  true  position  lat. 
39°  37'  N.,  long.  39°  36'  30"  W.  The  lat.  by 
D.  R.  was  7'  45"  in  error. 


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Lot.  39°45'N 


GREAT-CIRCLE  SAILING 

It  is  a  peculiar  fact  that  on  a  Mercator's 
chart  a  straight  course  between  two  places 
appears  as  a  curve.  This  is  owing  to  the 
expansion  of  the  degrees  of  lat.  and  long, 
towards  the  poles,  in  order  to  construct 
the  chart  on  the  theory  that  the  earth  is  a 
cylinder,  as  already  explained.  The  con- 
verse is  equally  true :  that  a  straight  line 
ruled  on  a  Mercator's  chart  is  really  a  curve 
when  you  come  to  sail  on  it. 

This  is  easily  seen  when  you  draw  the 
two  lines  on  flat  or  spherical  surfaces.  As 
the  meridians  of  longitude  constantly  con- 
verge towards  the  poles,  and  as  courses 
are  all  measured  by  the  angles  they  make 
with  the  meridians,  it  naturally  follows  that 
when  you  draw  the  meridians  all  parallel 
to  one  another,  you  must  be  distorting  an 
actual  course  when  you  make  it  cut  all 
these  meridians  at  the  same  angle.  Drawn 
on  a  sphere,  your  straight  course  would  be- 
come a  curve,  known  as  a  rhumb  line. 
;See  page  174.) 

Great-circle  charts  can  be  obtained,  and 
on  them  all  great-circle  tracks  appear  as 
straight  lines.  But  Sir  George  Airy,  As- 


tronomer  Royal  of  Great  Britain,  designed 
a  method  of  drawing  a  correct  great-circle 
track  on  a  Mercator's  chart.  His  method 
is  as  follows : 

Connect  the  point  of  departure  and  that 
of  destination  by  a  straight  line,  and  find 
by  measurement  the  centre  of  the  line. 


175 


Draw  from  this  central  point,  at  right  an- 
gles to  the  line  first  drawn,  a  second  line,  and 
continue  it  beyond  the  equator  if  necessary. 

With  the  middle  lat.  between  the  two 
places  enter  the  appended  table,  and  take 
out  the  lat.  under  "  corresponding  paral- 
lel." The  perpendicular  line  must  reach 
and  intersect  this  parallel. 

Now  put  one  point  of  the  dividers  in  this 
intersection,  and  with  the  other  point  de- 
scribe a  curve  which  will  pass  through  the 
point  of  departure  and  that  of  destination. 
This  curve  will  be  the  great-circle  track. 


Middle 
Lat. 

Corresponding  Parallel 
opposite  Name  to 
Lat.  of  Places 

Middle 
Lat. 

Corresponding  Parallel 
same  Name  as  Lat.  of 
Places 

200 

81°  13' 

* 

* 

22° 

780  16' 

* 

* 

24° 

74°  59' 

* 

* 

26° 

28° 

710  26' 
67°  38 

* 
50° 

# 
4°oo' 

30o 

63°  37' 

600 

9°i5' 

32o 

59°  25 

62° 

I40   32^ 

55°  05 
50°  36 

64o 
66° 

25°  09' 

38° 

460  oo' 

68° 

30°  30' 

4°o 

41°  18' 

70° 

35°  52' 

36°  3'' 

72° 

41°  14' 

loo 

3i°  38' 
26°  42' 

74°                46°  37' 
76°   i               52°  oi  ' 

48n 
50° 

21°  42' 

16°  39' 

78° 
80° 

62°  51' 

52° 

11°  33' 

* 

* 

54° 

6°  24; 

* 

* 

56° 

i°  13' 

* 

s76 


The  blank  spaces  arise  from  the  fact  that 
in  such  relations  great-circle  sailing  is  of 
no  advantage.  Within  the  tropics,  for  in- 
stance, it  is  of  little  use,  because  the  dis- 
tortion of  the  degrees  on  a  Mercator's 
chart  is  so  small. 

A  ship  on  a  great -circle  track,  except 
when  on  the  equator  or  sailing  N.  or  S. 
true,  must  change  her  course  often  in  order 
to  keep  on  the  track.  Here  the  principle 
that  a  small  arc  of  a  large  circle  on  the 
earth's  surface  is  practically  a  straight  line 
may  be  employed,  and  the  successive 
courses  laid  off  as  usual  with  parallel  rules 
and  dividers.  You  may  find  the  distance 
on  a  great-circle  course  with  close  approx- 
imation by  computing  the  lengths  of  these 
short  courses  and  adding  them. 

To  find  the  courses  to  be  sailed,  get  the 
difference  between  the  course  at  starting 
and  that  at  the  middle  of  the  circle,  and 
find  how  many  quarter-points  are  contained 
in  it.  Divide  the  distance  of  half  the  great 
circle  by  this  number  of  quarter-points, 
and  that  will  give  the  number  of  miles  to 
sail  on  each  quarter-point  course. 

Suppose  the  course  at  starting  to  be 
N.E.,and  at  the  centre  E.N.E.,and  the  dis- 


tance  from  start  to  centre  800  miles.  The 
difference  between  N.E.  and  E.N.E.  is  2 
points,  which  =  8  quarter-points.  Divide 
800  by  8,  and  you  get  100  miles  for  each 
quarter  -  point  course.  In  other  words, 
every  100  miles  you  change  the  true  course 
a  quarter  of  a  point  easterly. 

Bear  in  mind  that  this  means  true  course. 
Compass  course  must  allow  for  variation 
and  deviation. 

Accurate  method  of  measuring  the  dis- 
tance on  a  G.-C.  track. —  Turn  the  largest 
course  (always  one  of  the  end  courses) 
into  degrees.  Then  add  the  cosec.  of  the 
largest  course,  cosine  of  the  smallest  lat., 
and  sine  of  the  diff.  of  long,  between  the 
two  places.  Answer  will  be  sine  of  the 
distance  in  degrees  and  minutes.  As  these 
are  degrees  and  minutes  of  a  great  circle, 
which,  like  the  equator,  extends  around  the 
full  circumference  of  the  earth,  multiply 
the  degrees  by  60  and  add  the  minutes, 
and  the  result  is  the  distance  required. 

If  the  sine  of  the  distance  gives  more 
than  90°,  subtract  the  angle  from  1 80°,  and 
use  the  sine  of  the  remainder. 


DISTANCE   AND   DANGER  ANGLES 

If  near  a  coast,  it  is  imperatively  neces- 
sary that  the  navigator  should  have  quick 
and  certain  methods  of  ascertaining  his 
distance  from  well-marked  points,  and  of 
avoiding  hidden  dangers  set  down  on  the 
chart. 

When  a  light  or  a  mountain  first  ap- 
pears above  the  horizon,  its  bearing  should 
at  once  be  taken  by  compass,  and  the  nav- 
igator should  consult  Table  VI.,  Bowditch, 
which  gives  the  distance  at  which  elevated 
objects  can  be  seen  at  sea.  The  height  of 
the  object  when  first  seen  above  the  hori- 
zon and  the  height  of  the  observer  must 
both  be  taken  into  account.  Thus : 

At  sea,  running  for  Block  Island  Chan- 
nel, Block  Island  Light,  204  ft.  above  the 
level  of  the  sea,  appeared  above  the  hori- 
zon. Observer  on  bridge  25  ft.  above  sea. 
Required  distance  of  light. 

Table  VI.  .200  ft.=  18.63  miles'  range  of  visibility. 
"  ..  25ft.=  6.59 

25.22  miles,  distance  of  light. 

Uncommon  refraction  will  sometimes  make 
a  light  appear  sooner  than  it  ought  to,  and 


'79 


the  navigator  must  be  on  the  lookout  for 
such  phenomena.  In  fact  the  whole  oper- 
ation is  not  to  be  accepted  as  infallible,  for 
at  the  best  it  gives  uncertain  results. 

The  vertical  angle  of  an  object  above 
the  water-line,  measured  by  the  sextant, 
may  also  be  used  to  give  the  distance. 
The  navigator  should  possess  Captain 
Lecky's  Danger  Angle  and  Off- Shore  Dis- 
tance Tables,  in  which  are  given  the  sex- 
tant angles  for  heights  up  to  1000  ft.  The 
vertical  angle  can  be  used  with  these  ta- 
bles when  the  object  is  partly  below  the 
horizon,  or  when  it  is  between  the  hori- 
zon and  the  observer.  A  handy  set  of 
vertical  danger -angle  tables  is  included 
in  Captain  Howard  Patterson 's  Navigator  s 
Pocket  Book.  If  the  object  is  far  away, 
and  the  angle  consequently  very  small,  it 
should  be  measured  both  on  and  off  the 
arc.  For  instance,  with  a  light-house,  first 
bring  down  the  centre  of  the  lantern  (just 
as  you  would  bring  the  sun)  to  the  hori- 
zon, and  read  the  angle.  Then  bring  up 
the  horizon  line  to  the  centre  of  the  lan- 
tern by  moving  the  index  bar  of  the  sex- 
tant towards  you,  and  read  that  angle. 
Take  the  mean  of  the  two,  and  enter  the 


tables  under  the  height  of  the  light.  Op- 
posite the  sextant  angle  (or  the  nearest 
one  to  it)  take  out  the  distance.  With  a 
mountain  bring  down  the  top  to  the  hori- 
zon. If  the  object  is  between  you  and  the 
horizon,  use  the  object's  water-line. 

Example:  Oct.  5,  1894,  bound  west,  pass- 
ingShinnecockLight,bearingN.-by-W.iW. 
by  compass,  desired  to  know  distance  of 
ship  from  it.  Vertical  sextant  angle,  from 
centre  of  light  to  water-line,  measured  on 
and  off,  22'  45". 

In  table  under  160  ft.  and  opposite  22' 
50",  distance  given  is  4  miles. 

Aboard  U.  S.  men-of-war  the  Bradley 
Fiske  range  -  finder  may  be  used  to  find 
the  distance  of  any  object  on  shore  not 
beyond  its  limits. 

For  passing  concealed  dangers  the  ver- 
tical sextant  angle  is  used  thus:  Suppose 
that  300  yards  to  the  eastward  of  a  light 
45  ft.  high,  which  you  must  pass  on  the 
easterly  side,  lies  a  shoal  spot  or  a  reef 
dangerous  to  you.  You  therefore  decide 
to  pass  300  yards  outside  of  it,  or  600  yards 
from  the  light.  Under  45  ft.  and  opposite 
600  yards  you  find  the  angle  i°  26'.  You 
set  the  sextant  at  that  angle,  and  watch 


i8t 


for  the  image  of  the  light  in  the  horizon- 
glass*  As  long  as  the  angle  between  the 
light  and  the  water-line  is  i°  26'  or  less, 
you  are  600  yards  or  more  from  the  light. 
If  the  angle  becomes  more,  you  are  inside 
of  600  yards.  You  need  not  move  the  in- 
dex bar  at  all,  for  if  the  light  rises  above 
the  water-line  as  seen  in  the  horizon-glass, 
the  angle  is  larger  than  that  set,  and  in 
this  case  that  means  danger ;  but  if  it  drops 
below,  the  angle  is  smaller. 

This  same  method  of  angling  is  used  in 
keeping  the  distances  between  war-ships 
steaming  in  squadron.  At  night  each  ship 
carries  a  white  light  at  her  fore-truck,  and 
the  angular  elevation  of  this  light  is 
watched.  In  daytime  keep  the  truck  it- 
self at  the  water-line.  The  elevation  of 
the  mast  is  known.  Ships  in  squadron 
always  keep  memoranda  of  the  angles  of 
their  consorts  for  distance,  half-distance, 
and  double-distance.  The  masthead  angle 
can  also  be  used  to  set  a  target  at  a  given 
distance  from  the  ship. 

The  horizontal  danger  angle  is  at  times 
extremely  valuable,  and  the  navigator 
should  master  its  use.  It  is  first  necessary 
to  learn  to  take  horizontal  angles  with  the 


sextant.  Hold  the  instrument  face  up. 
Look  through  the  sight-vane  and  horizon- 
glass  at  the  left-hand  object,  and  push  the 
index  bar  forward  till  the  right-hand  ob- 
ject makes  contact  with  it.  Then  read  the 
angle. 

It  is  a  good  plan  to  take  cross-bearings 
this  way,  noting  the  compass  bearing  of 
one  of  the  objects.  The  bearing  of  the 
other  is  at  once  known  by  the  angle  be- 
tween the  two.  If  the  ship's  head  should 
fall  off  between  the  bearings,  and  change 
the  deviation,  you  would  have  only  one 
deviation  to  apply. 

The  horizontal  danger  angle  is  used  in 
passing  hidden  dangers.  Suppose  you  wish 
to  pass  at  a  distance  of  a  quarter  of  a  mile 
outside  of  some  hidden  rocks,  and  on  the 
shore  are  certain  objects,  say  a  light-house 
and  a  mountain,  marked  on  the  chart.  Draw 
a  circle  around  the  rocks  with  a  radius  of 
a  quarter  of  a  mile.  Now  describe  anoth- 
er circle  that  will  pass  through  the  light- 
house, the  church,  and  the  most  seaward 
part  of  your  first  circle.  From  this  last 
point,  A,  draw  lines  to  the  light-house  and 
the  church.  Now  measure  with  a  pro- 
tractor the  angle  at  the  juncture  of  these 


two  lines.  Set  that  angle  (47*  in  the  dia- 
gram) on  the  sextant,  and  watch  the  se- 
lected objects  with  instrument  face  up. 
The  moment  your  two  objects  appear  in 
the  horizon  -  glass  you  are  close  to  your 
circle  of  safety,  and  when  they  make  con- 
tact you  are  on  it.  All  you  have  to  do  is 
to  alter  the  course  of  the  ship  so  as  to 
keep  the  contact,  and  so  sail  around  the 
outer  part  of  your  circle  till  you  have 
rounded  the  rocks.  If  you  watch  the  angle 
closely  this  cannot  fail,  and  in  narrow  wa- 
ters it  is  an  invaluable  method. 

In  measuring  vertical  danger  angles  get 
as  close  to  the  water  as  possible,  so  as  to 


i84 


remove  error  caused  by  your  height  above 
the  water.  This  error,  however,  will  in- 
crease your  angle  and  thus  place  you  far- 
ther away  from  the  danger ;  so  that  you 
will  be  all  right  unless  you  have  a  second 
danger  close  aboard  on  the  other  side. 


ALLOWANCE   FOR  TIDES 

In  fixing  positions  by  lights,  mountains, 
etc.,  in  passing  over  shoals,  and  in  berthing 
ship  at  anchorage,  bear  in  mind  that  heights 
are  recorded  on  charts  as  measured  from 
high- water,  ordinary  spring  tides,  while 
soundings  are  for  mean  /^w-water. 

To  find  the  rise  of  the  tide  or  its  fall.— 
Use  the  following  diagram  : 


The  right-hand  side  shows  how  the  tide 
falls  =  i  of  its  range  for  the  first  hour,  J  at 
the  end  of  the  second,  £  at  the  end  of  the 
third,  and  so  on.  The  left-hand  side  shows 
how  it  rises. 

Remember  that  the  rise  and  fall  do 
not  coincide  with  the  change  of  tidal  cur- 
rent. You  must  ascertain  the  duration 
of  the  ebb  and  flow  from  published  sail- 
ing directions,  such  as  the  Atlantic  Coast 
Pilot. 

Where  the  range  of  the  tide  is  great,  you 
must  allow  for  it  in  measuring  angular  al- 
titudes of  shore  marks. 

KEEPING  THE  LOG 

A  log-book  contains  the  record  of  the 
day's  work  of  the  ship.  It  may  be  made 
very  simple  or  very  elaborate.  The  ordi- 
nary merchant  service  log-book  is  quite 
simple.  The  data  to  be  put  in  the  book 
are  noted  on  a  log-slate  by  the  watch  offi- 
cers and  afterwards  transferred  to  the  log- 
book. A  simple  and  satisfactory  form  of 
log  is  as  follows : 


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The  hours,  contained  in  the  first  column, 
are  numbered  from  noon  till  noon.  The 
second  column  contains  the  knots,  and  the 
third  the  fathoms,  which  are  eighths  of 
knots.  The  entries  to  be  made  in  the  re- 
maining columns  are  perfectly  apparent. 
Winds  should  never  be  entered  in  frac- 
tions, but  in  whole  points. 

The  form  of  log  used  in  the  U.  S.  navy 
is  exhaustive.  The  log  is  kept  by  the 
watch  officers  in  a  "  rough-log  "  book,  and 
afterwards  copied  in  the  official  book  by 
the  ship's  writer.  Each  officer  signs  that 
part  of  the  log  for  which  he  is  responsi- 
ble with  his  full  name  and  rank.  Junior 
watch  officers  record  the  readings  of  the 
barometer  and  thermometers,  state  of 
weather,  forms  of  clouds,  proportion  of 
clear  sky,  and  condition  of  sea.  (See  ta- 
ble on  next  page.)  Then  follows  the  form 
for  the  remaining  12  hours,  which  is  simi- 
lar. These  forms  fill  the  left-hand  page. 
The  right-hand  page  is  headed  "  Record  of 
Miscellaneous  Events  of  the  Day,"  and  con- 
tains the  running  record  of  the  business 
and  weather  of  each  watch. 


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RATING   A   CHRONOMETER 

It  is  sometimes  necessary  on  a  long  voy- 
age to  ascertain  the  daily  gain  or  loss  of 
the  chronometer,  owing  to  the  fact  that 
the  rate  may  be  affected  by  extremes  of 
temperature  or  other  causes.  The  navi- 
gator may  be  far  away  from  a  maker,  and 
hence  must  know  how  to  ascertain  the 
rate  for  himself.  To  perform  the  opera- 
tion he  will  require  an  artificial  horizon. 
This  consists  of  a  small  trough,  which  is 
filled  with  absolutely  clean  mercury,  and 
covered  with  a  glass  case  which  permits 
the  observer  to  see  the  reflecting  surface, 
and  yet  keeps  wind  and  dust  away  from  it. 

The  observer  must  now  go  with  his  sex- 
tant, chronometer,  and  artificial  horizon  to 
a  spot  where  the  longitude  is  accurately 
known  to  a  fraction  of  a  second.  This 
will  obviously  be  on  shore,  and  that  is  why 
the  artificial  horizon  must  be  used. 

The  observer  should  station  himself,  sit- 
ting, if  possible,  so  that  the  artificial  hori- 
zon will  be  in  a  direct  line  between  him- 
self and  the  body  to  be  observed,  and  the 
image  of  the  body  will  be  shown  in  the 
mercury.  Look  through  the  sight-vane  of 


the  sextant,  so  as  to  see  the  image  in  the 
mercury  through  the  horizon-glass.  Bring 
down  the  image  reflected  by  the  sextant 
mirror  till  it  makes  contact  with  the  image 
in  the  mercury.  At  that  instant  note  the 
chronom.  time. 

The  angle  of  altitude  shown  by  the  sex- 
tant will  be  double  what  it  would  be  with 
a  sea  horizon,  and  must  therefore  be  di- 
vided by  2.  The  altitude  is  corrected  as 
usual,  except  for  height  of  the  eye,  which 
does  not  exist  in  this  operation. 

The  remainder  of  the  operation  consists 
of  finding  the  local  mean  time,  and,  by  ap- 
plying the  longitude,  the  correct  G.  M.  T. 
at  the  instant  of  observation.  Thus  the 
error  of  the  chronom.  is  found.  The  ob- 
server now  waits  not  less  than  six  days 
(ten  days  are  better),  and  then  repeats  the 
process  at  the  same  place.  From  the  dif- 
ference in  the  error  on  the  two  dates  you 
get  the  daily  rate. 

For  instance,  suppose  that  on  May  2, 
1894,  at  Falmouth,  Eng.,  you  set  out  to  rate 
your  chronom.  with  artificial  horizon  and 
the  sun.  Your  altitude,  worked  out  accord- 
ing to  the  rule  for  a  chronom.  sight,  gives 
you  app.  time  at  Falmouth  6  hrs.,  53  min., 


22  sec.  A.M.  Apply  the  corrected  equation 
of  time  and  get  Falmouth  M.  T.,  6  hrs.,  50 
min.,o7.8  sec.  The  longitude  of  Falmouth 
is  5°  02'  W.  =  20  min.,  08  sec.  Add  this  to 
Falmouth  M.  T.  and  you  get  7  hrs.,  10  min., 
1 5.8  sec.  G.  M.  T.  At  the  instant  of  obser- 
vation the  chronom.  showed  7  hrs.,  18  min., 
1 8  sec.  A.M.  ;  chronom.  fast  of  G.  M.  T.,  8 
min.,  02. 2  sec. 

On  May  8  you  repeat  the  process,  and 
find  that  the  chronom.  is  8  min.,  05.2  sec. 
fast  of  G.  M.  T. 

May  2 8m.  02.25. 

May  8 8        05.2 

Gain  in  6  days 3  s.=  Daily  rate  0.5  s. 

Of  course  you  can  use  the  stars  or  plan- 
ets for  this  work  just  as  well  as  the  sun. 
Whatever  you  use,  bear  in  mind  these 
facts :  If  the  celestial  body  is  rising  (east 
of  meridian),  the  two  images  seen  through 
the  horizon  -  glass  will  separate,  provided 
you  are  using  the  lower  limb.  If  the  body 
is  sinking  (west  of  meridian), they  will  close. 

Chronometers  may  be  rated  in  many 
ports  without  observation  by  means  of 
public  time  signals,  such  as  time  balls  or 
guns,  which  mark  a  given  hour  either  of 
local  or  G.  M.  T. 


CARE   OF   A    CHRONOMETER 

\Condensed,  by  permission  of  T.  S.  andj.  D.  Negus,  from 
their  paper  read  before  the  Naval  Institute) 

Be  careful  in  carrying  a  chronometer 
tiever  to  give  it  a  horizontal  twist.  This 
motion  will  affect  the  balance  to  such  an 
extent  as  to  throw  the  chronometer  a  sec- 
ond or  a  second  and  a  half  out  of  time. 

The  gimbals  must  be  secured  so  as  to 
prevent  the  chronometer  from  swinging 
while  being  carried.  There  is  a  stay  for 
this  purpose.  Aboard  ship  the  instrument 
should  be  allowed  to  swing. 

Keep  a  chronometer  aboard  ship  always 
in  its  outside  case,  in  an  apartment  well 
ventilated,  yet  free  from  draughts.  Never 
put  a  chronometer  near  wood  which  is  in 
contact  with  salt-water. 

Never  open  the  outside  case  except 
when  winding  or  taking  time. 

In  damp  countries  wrap  a  blanket  around 
the  outside  case. 

You  cannot  do  too  much  to  protect  a 
chronometer  from  rust.  A  small  spot  will 
change  the  rate  of  the  instrument. 

Wind  the  chronometer  every  day  at  the 
same  hour,  unless  it  is  an  eight-day  chro- 


nometer ;  then  wind  it  once  every  week  at 
the  same  time. 

In  winding,  turn  the  chronometer  bowl 
over  in  the  gimbal  slowly  with  the  left 
hand,  slide  the  valve  by  pressing  the  fore- 
fingers of  the  left  hand  against  the  nail- 
piece  on  the  valve  until  the  key  -  hole  is 
uncovered,  insert  the  winding  key  with  the 
right  hand,  and  wind  to  the  left  till  a  de- 
cided stop  is  felt.  After  removing  the  key, 
do  not  let  the  chronometer  of  its  own  ac- 
cord drop  to  its  level,  but  let  it  down  care- 
fully until  horizontal. 

Never  let  a  chronometer  get  within  the 
magnetic  influence  of  a  compass  or  an 
electro-magnet. 

If  a  chronometer  has  run  down  and  needs 
to  be  started,  wait  till  the  hands  indicate 
the  proper  time,  and  then  start  it  by  a 
slight  horizontal  twist. 

All  chronometers  reach  their  highest 
gaining  or  losing  rate  at  a  certain  tem- 
perature. Those  used  in  the  United  States 
Navy,  made  by  Negus,  reach  their  fastest 
rate  at  70°  F.  Any  exposure  of  the  instru- 
ment to  other  temperatures  will  change 
the  rate.  The  average  temperature  cor- 
rection, as  given  by  the  makers,  is  .0025 


'94 


second,  multiplied  by  the  square  of  the  dif- 
ference in  the  number  of  degrees  of  tem- 
perature. Thus,  to  find  the  correction  to 
be  made  to  the  rate  of  a  chronometer  in 
a  temperature  of  80°,  multiply  .0025  by  the 
square  of  the  difference  between  70°  and 
80°.  A  chronometer  with  a  rate  of  -}-1 
sec.  at  70°  would  show  the  following  vari- 
ations : 

55°         60°         65°         70° 
+  -4375S.     +-75S.     +-93758.     +  1 8. 

75°         80°         85° 
+  -9375S.     +-75S.     -f  .4375  s. 

Chronometers  should  be  cleaned  and 
oiled  at  least  once  every  three  years  and  a 
half. 

Vessels  destined  for  long  voyages  should 
carry  three  chronometers.  If  you  have 
two  and  one  goes  wrong,  you  cannot  tell 
which  is  in  error.  With  three  you  can 
make  daily  comparisons  and  know  pretty 
well  what  they  are  doing. 

Keep  your  chronometers  away  from  iron. 
It  affects  the  going  of  the  instruments. 

If  you  have  to  carry  a  chronometer,  use 
the  leather  strap  attached  to  the  case,  and 
be  careful  not  to  swing  the  instrument  or 
let  it  knock  against  anything. 


'95 


In  transporting  a  chronometer  overland 
(by  rail,  for  instance),  put  it  in  a  basket 
resting  on  plenty  of  cotton  or  some  other 
substance  that  will  keep  it  from  jarring. 


HINTS   ON   CONDUCTING  VOYAGES 

Before  leaving  port  ascertain  the  exact 
draught  of  your  vessel.  Also  ascertain  the 
height  of  your  eye  above  the  water-line  at 
all  points  available  for  taking  observa- 
tions. 

As  soon  as  you  are  on  open  water  fix 
the  position  of  the  ship  by  cross-bearings, 
by  vertical  or  horizontal  angle  and  com- 
pass bearing,  or  by  compass  and  range- 
finder. 

This  is  called  taking  departure,  and  is 
entered  in  the  log  opposite  the  hour  thus: 
"  Sandy  Hook  Lightship  bearing  S.  15°  W., 
distant  2  miles,  from  which  I  take  de- 
parture." 

From  the  moment  of  taking  departure 
begin  the  record  of  the  course  and  dis- 
tance for  each  hour  in  the  log-book. 

Enter  the  regulation  noon  position  in 
the  log  every  day;  but  get  a  ''good  fix," 


196 


as  it  is  called,  at  other  times,  especially  in 
the  mid  and  morning  watches.  If  the  sun 
fails  to  come  to  time  the  following  morn- 
ing and  noon,  you  will  be  glad  you  shot 
the  stars. 

As  soon  as  you  take  departure  set  the 
first  course  of  your  great  circle,  if  on  one, 
or  your  Mercator's  course.  If  under  sail, 
select  the  course  which  lies  nearest  to  the 
great-circle  track. 

Work  out  your  dead-reckoning  traverse 
up  to  noon  every  day,  and  enter  the  re- 
sults in  the  proper  places  in  the  log. 

When  approaching  the  land  be  keen  to 
note  every  indication  of  its  proximity. 
Look  out  for  floating  vegetation,  change 
in  the  color  of  the  water  from  sea  blue  to 
muddy  green,  flight  of  land  birds,  butter- 
flies, etc. 

Make  it  a  cast-iron  rule  invariably  to  fix 
the  ship's  position  by  Sumner's  method 
when  approaching  the  land.  If  you  can 
get  a  good  line  of  bearing  for  your  port — 
and  you  generally  can — get  on  it  and  stay 
there. 

As  soon  as  you  are  on  soundings  start 
the  sounding-machine  or  deep-sea  lead  go- 
ing, and  keep  a  record  of  the  time  of  each 


197 


cast,  with  depth  of  water  and  character  of 
bottom,  and  course  and  distance  between 
casts,  to  compare  with  the  chart.  Many  a 
first-class  officer  has  lost  his  ship,  his  li- 
cense, and  his  occupation  from  neglect  to 
use  the  lead,  and  there  is  no  hope  for  a 
man  proved  guilty  of  it  before  a  court  of 
inquiry. 

Never  attempt  to  pass  close  to  hidden 
dangers  when  there  are  no  landmarks  near. 
Remember  the  history  of  the  Roncador 
Reefs.  Give  such  traps  a  wide  berth. 

As  soon  as  land  is  sighted  fix  the  posi- 
tion of  the  ship  as  often  as  possible  by  bear- 
ings and  distances  of  mountains,  lights,  etc. 

Remember  that  you  can  never  be  too 
sure  of  your  position.  Eternal  vigilance 
is  the  price  of  safety  at  sea,  and  dangers 
increase  with  the  approach  to  land. 

Do  not  be  discouraged  if  your  first  cal- 
culations are  considerably  abroad.  Sir 
Thomas  Brassey's  first  landfall  was  60 
miles  in  error ;  but  he  learned  to  take  his 
yacht  around  the  world.  It  takes  time 
and  practice  to  become  an  expert  navi- 
gator, but  any  man  of  ordinary  intelligence 
can  be  one  if  he  perseveres. 


EXAMPLES  FOR   PRACTICE 

DEAD-RECKONING 

Suppose  a  ship  to  sail  upon  the  follow- 
ing courses  and  distances:  S.E.-by-S.,  29 
miles;  N.N.E.,  10;  E.S.E.,  50;  E.N.E.,  50; 
S.S.E.,  10 ;  N.E.-by-N.,  29;  WM  25  ;  S.S.E., 
10 ;  W.S.W.iW.,  42 ;  N.,  1 10 ;  Ef  N.,  62  ;  N., 
7;  W.,  62;  N.,  10;  W.,  8;  S.,  10;  W.,  62; 
S.,  7;  E.JS.,  62;  S.,  no;  W.N.W.fW.,  42; 
N.N.E.,  10 ;  and  W.,  25.  Required  the 
course  and  distance  made  good  (Norie). 

Ans.  The  ship  has  returned  to  the  place 
she  started  from. 

From  lat.  40°  3'  N.,  long.  73°  28'  W., 
ship  sails  S.E.-by-S.,  36  miles,  variation  \ 
pt.  west ;  S.E.-by-S.,  8  miles,  variation  J  pt. 
west;  S.E.iE.,  28  miles,  with  half  a  point 
of  leeway  on  the  starboard  tack  and  varia- 
tion J  pt.  west.  Ship  has  been  8  hrs.  in 
a  current  setting  N.E.  (variation  J  pt.  W.) 
at  the  rate  of  2  knots  per  hr.  Required 
lat.  and  long,  in  and  course  and  distance 
made  good  (Patterson). 

Ans.  Lat.  39°  26'  N.,  long.  72°  07'  W., 
course  S.  60°  E.,  dist.  72  miles. 


SHAPING  COURSE  BY  MERCATOR'S  SAILING 

Required  the  bearing  and  distance  of 
Pernambuco,  lat.  8°  4'  S.,  long.  34°  53'  W., 
from  Cape  Verde,  lat.  14°  45'  N.,  long.  17° 
32'  W.  (Norie). 

Ans.  S.  37°  W.,  dist.  1715  miles. 

Required  course  and  distance  from  Cape 
Palmas,  lat.  4°  24'  N.,  long.  7°  46'  W.,  to  St. 
Paul  de  Loando,  lat.  8°  48'  S.,  long.  13°  8'  E. 
(Norie). 

Ans.  S.  58°  E.,  dist.  1481  miles. 


LATITUDE   BY  MERIDIAN   ALTITUDE  OF 

SUN 

At  sea,  merid.  alt.  0  38°  15'  15"  S. ,  I.  E., 
1°  10'  — ;  H.  of  E.,  1 5  ft. ;  chronom.,  4  hrs., 
10  min.,  1 8  sec.  P.M.  ;  chronom.  slow  of  G. 
M.  T.  4  min.,  37  sec. ;  dec.,  15°  27'  13"  N., 
increasing  ;  hourly  var.,  44.6".  Required 
lat.  of  ship. 

Ans.  68°  14'  N. 

At  sea,  merid.  alt.  O  53°  52'  S. ;  I.  E., 
—3'  24" ;  H.  of  E.,  24  ft. ;  G.  M.  T.,  4  hrs., 
54  min.,  10  sec.  P.M.  ;  dec.,  2°  47'  3.5"  N.,  de- 


creasing ;  hourly  var.,  57.9".  Required  lat. 
of  ship. 

Ans.  38°  43'  N. 

At  sea,  merid.  alt.  Q  48°  18'  15"  N. ;  I.  E., 
-2'  15" ;  H.  of  E.,  20  ft. ;  G.  M.  T.,  10  hrs., 
26  min.,  15  sec.  A.M.  ;  dec.,  19°  26'  S.,  de- 
creasing; hourly  van,  35.5".  Required  lat. 
of  ship. 

Ans.  61°  if  S. 

At  sea,  merid.  alt.  0  59°  45' 45"  N. ;  I.  E., 
+  30'  15" ;  H.  of  E.,  15  ft. ;  G.  M.  T.,  6  hrs., 
14  min.,  20  sec.  A.M.  ;  dec.,  4°  15'  12"  N.,  in- 
creasing ;  hourly  van,  58". 

Ans.  25°  22'  S. 


LATITUDE   BY   MERIDIAN   ALTITUDE  OF 
STAR 

At  sea,  Dec.  24,  1894.  Merid.  alt.  *  Al- 
debaran  52°  36'  S. ;  no  I.  E. ;  H.  of  E.,  20 
ft.;  dec.  of*  16°  17'  52"  N.  Required  lat. 
of  ship. 

Ans.  53°  47i'  N. 

At  sea,  Dec.  26,  1894.  Mend.  alt.  Sirius 
36°28'S.;  I.E.,  —  45";  H.of  E.,  14  ft. ;  dec. 
of  *,  16°  34'  20'  S.  Required  lat.  of  ship. 

Ans.  37°  3'  N. 


LATITUDE    BY    MERIDIAN    ALTITUDE    BE- 
LOW THE  POLE 

At  sea,  April  10, 1885.  Merid.  alt.  *  Cano- 
pus  below  pole,  22°  38'  S. ;  dec.,  52°  37'  59" 
S,;  I.  E.,  +  2' ;  H.  of  E.,  18  ft.  Required  lat. 
of  ship  (Sturdy). 

Ans.  59°  55'  39"  S. 

At  sea,  June  18,  1885.  Obs.  merid.  alt. 
0  below  pole,  8°  10'  20";  dec.  at  time  of 
obs.,  23°  25'  57"  N. ;  I.  E.,  +  3' ;  H.  of  E.,  20 
ft.  Required  lat.  of  ship  (Sturdy). 

Ans.  74°  52'  N. 


LATITUDE  BY  EX-MERIDIAN  ALTITUDES 

At  sea,  July  12,  1885.  Lat.  by  D.  R.  50° 
N.,  long,  by  D.-R.  40°  W. ;  obs.  ex-merid.  alt. 
©6i°48'3o";  I.E., -3';  dip,  3' 48";  G.M.T. 
of  obs.,  2°  39'  9";  dec. of  ©  21°  55'  36"  N.; 
hourly  diff.  dec.,  21.22",  dec.  decreasing; 
equation  of  time  to  be  subtracted  from  M. 
T.,  5  min.,  20.7  sec. ;  hourly  diff.  equation, 
.314",  equation  decreasing.  Required  lat. 
of  ship  (Sturdy). 

Ans.  49°  56'  N. 

At  sea,  June  6,  1880.     Lat.  by  D.  R.  49° 


21'  N.,  long.  18°  18'  W. ;  obs.  ex-merid.  alt. 
*  Arcturus,  59°  41'  S. ;  dec.  of*  19°  48'  15" 
N. ;  no  1.  E. ;  H.  of  E.,  22  ft. ;  G.  M.  T.,  9 
hrs.,  46  min. ;  G.  Sid.  T.  preceding  noon,  5 
hrs.,  i  min.,  6  sec. ;  R.  A.  of  *  14  hrs.,  10 
min.,  14  sec.  Required  lat.  of  ship  by  <£' 
and  <t>"  sight  (Lecky). 
Ans.  49°  23J'  N. 

LATITUDE   BY  THE  POLESTAR 

At  sea,  June  21, 1880.  Lat.  by  D.  R.  45° 
20'  N.,  long.  37°  57'  W. ;  obs.  alt.  of  Polaris, 
44°  13'  30"  N. ;  I.  E.,  +  30" ;  H.  of  E.,  32  ft. ; 
G.  M.  T.,  11°  45'  20";  G.  Sid.  T.  preceding 
noon,  6  hrs.,  14  sec.  Required  lat.  of  ship 
(Lecky). 

Ans.  45°  17'  N. 

LONGITUDE   BY  CHRONOMETER  SIGHT 

Observed  A.M.  alt.  0  20°  30' ;  chronom. 
i  hr.,  ii  min.,  19  sec.  P.M.;  chronom.  10 
min.,  20  sec.  fast;  H.  of  E.,  10  ft. ;  lat.  by 
D.  R.  40°  15'  N. ;  dec.  at  noon,  13°  26'  6" 
S. ;  hourly  diff.  dec.,  50.36",  dec.  decreas- 
ing; equation  of  time,  14  min.,  27.66  sec.; 


203 


hourly  diff.  equation,  .055",  equation  de- 
creasing; equation  to  be  added  to  app. 
time.  Required  long,  of  ship  (Patterson). 

Ans.  58°  59'  45"  W. 

At  sea,  Jan.  22,  1895.  Obs.  alt.  of  O  A.M. 
17°  14';  G.  M.  T.,  n  hrs.,  42  min.  A.M.; 
H.  of  E.,  20  ft. ;  no  I.  E. ;  lat.  38°  50'  N. ; 
dec.  at  noon,  23°  33''  S. ;  hourly  diff.,  12.48' 
dec.  decreasing;  equation  of  time  (to  be 
subtracted  from  mean  time),  3  min.,  46.42 
sec. ;  hourly  diff.  equation,  1.183  sec-»  equa- 
tion increasing.  Required  long,  of  ship. 

Ans.  Long.  34°  18'  30"  W. 

At  sea,  Feb.  27,  1882.  Lat.  40°  10'  45" 
N. ;  H.  of  E.,  30  ft.;  no  I.  E. ;  obs.  alt.  * 
Procyon,  39°  u'  E. ;  G.  M.  T.,  9  hrs.,  58 
min.,  45  sec. ;  Sid.  T.  at  G.  at  preceding 
noon,  22  hrs.,  28  min.,  52  sec. ;  dec.  *,  5° 
31'  15"  N. ;  R.  A.  *,  7  hrs.,  33  min.,  10  sec. 
Required  long,  of  ship,  true  bearing  of  star, 
and  Sumner  line  (Lecky). 

Ans.  Long.  55°  40'  15"  W. ;  true  bearing 
of  star,  S.  58°  E. ;  Sumner  line,  N.  32°  E. 


204 


WAR-TIME  PROBLEMS 

The  problems  which  present  themselves 
to  the  navigator  in  war- time,  particularly 
when  he  is  near  a  coast,  are  of  especial  dif- 
ficulty and  demand  extreme  caution  in  their 
treatment.  Modern  warfare,  which  has 
brought  with  it  the  extensive  employment 
of  the  submarine  and  the  equally  extensive 
use  of  submarine-chasers  of  various  types, 
patrol  boats,  mine-sweepers,  and  other  craft, 
has  set  up  conditions  of  inshore  navigation 
quite  unknown  to  the  earlier  naval  officers. 

Since  it  must  be  obviously  the  policy  of  the 
United  States  Government  to  meet  the  new 
conditions  by  the  building  and  manning  of  an 
enormous  fleet  of  coast-patrol  vessels  of  the 
numerous  kinds,  to  be  kept  in  use  not  only 
in  the  present  war,  but  as  long  as  the  sub- 
marine menace  exists  to  threaten  vessels 
threading  the  narrow  seas  or  approaching 
the  coasts  of  the  great  ones,  it  becomes  im- 
perative that  the  officers  handling  the  pa- 
trol craft  shall  make  themselves  past-masters 
of  the  comparatively  new  problems  in 
navigation. 


205 

In  the  first  place  the  commander  of  a  patrol 
vessel  must  realize  the  indisputable  fact  that 
a  submarine  can  secretly  enter  an  unfre- 
quented bay  and  lie  concealed  in  some  small 
bight  or  inlet,  provided  there  is  water  enough 
to  float  her.  She  can  also  lie  on  the  bottom 
for  a  long  time.  That  submarines  will  do 
either  has  proved  to  be  the  case  over  and  over 
again  in  British  waters,  and  it  is  likely  to  be 
the  case  here,  especially  since  no  country  is 
wholly  free  from  disloyal  persons  who  would 
gladly  communicate  with  submarines  in  order 
to  give  them  information  or  stores. 

Again,  the  patrol  vessel  will  at  times  be 
glad  of  her  own  ability  to  find  concealment 
in  some  such  unfrequented  inlet  or  bay. 
One  of  the  first  duties,  then,  of  a  patrol  com- 
mander is  to  make  himself  absolute  master  of 
the  details  of  the  coast  which  he  patrols. 
All  the  information  which  he  ne.eds  will  not 
be  found  on  the  charts.  There  are  a  thousand 
tricks  of  the  local  tides,  for  example,  which 
only  the  local  man  knows.  For  instance,  in 
the  East  River  immediately  behind  Bellevue 
Hospital  the  flood  tide  sets  in  toward  the 
pier-head  instead  of  up  the  river.  Tugboat 
captains  all  know  a  thing  like  that.  Strangers 
do  not.  In  a  hundred  other  details  of  such 
kind  all  coastwise  navigation  carried  on  close 


206 

inshore  or  among  islands  abounds,  and  the 
stranger  can  easily  get  into  trouble  through 
ignorance  of  them. 

Local  fishermen  are  prolific  sources  of  in- 
formation in  regard  to  such  matters.  It  is  a 
part  of  their  business  to  know  them.  The 
patrol-boat  commander  should  draw  as  much 
of  such  information  as  he  can  get  from  the 
fishermen  who,  once  they  understand  the 
object  of  it,  will  give  it  readily  and  intelli- 
gently. Another  invaluable  set  of  men  from 
whom  to  acquire  this  kind  of  knowledge  is 
skippers  of  racing-yachts  of  the  locality. 

Having  gathered  every  possible  scrap  of 
information  of  this  kind,  the  patrol-boat 
commander  should  next  turn  his  attention  to 
all  kinds  of  landmarks  which  can  be  used  in 
establishing  a  position  when  in  sight  of  land. 
Here  the  fishermen  will  prove  invaluable,  for 
it  has  been  the  observation  of  the  author  that 
these  men  are  in  the  habit  of  utilizing  church 
spires,  water-towers,  etc.,  in  giving  them 
bearings  by  which  to  reach  points  desired. 
The  navigator  will  not  find  these  things  on 
his  chart,  but  he  can  put  them  there,  and  that 
is  what  I  advise  him  to  do.  Also  it  is  a  good 
plan  to  make  a  record  in  some  convenient 
place  of  the  exact  location  of  such  things  as 
railway  stations,  telegraph  and  post  offices, 


207 

coal-yards,    life-saving    stations,    and    shore 
hospitals  wherever  they  exist. 

ABSENCE   OF  LIGHTS  AND   BEACONS 

The  navigator  must  not  forget  that  in  war- 
time he  may  be  deprived  of  most  of  his 
familiar  lights  and  beacons.  War-time  often 
means  lights  out.  The  navigator  has  to 
transform  himself  into  a  marine  cat,  with 
eyes  that  can  see  in  the  dark.  Fortunately 
the  less  artificial  light  there  is  in  the  neighbor- 
hood the  better  a  man  can  see  at  night. 

But  in  alongshore  work  his  sight  will  be  of 
little  value  to  him  if  he  does  not  know  the 
sky-line  of  the  coast.  This  is  a  thing  which 
every  coast-patrol  officer  should  study  as- 
siduously. The  occasions  on  which  knowl- 
edge of  it  will  become  important,  even  vital, 
are  innumerable.  A  fisherman  of  Block 
Island,  for  example,  does  not  need  the  light 
on  the  south  end  of  the  island  to  assure  him 
that  he  is  not  running  in  for  Montauk  Point. 
The  loom  of  the  almost  indistinguishable  land 
in  the  blackness  of  the  night  will  tell  him  what 
he  needs  to  know  and  he  will  steer  with 
confidence. 

A  patrol  officer  working  along  the  New 
Jersey  shore  should  be  able  to  tell  from  the 


208 

shoulder  of  the  Highlands  precisely  how  to 
steer  to  get  the  Ambrose  Channel  buoy  or 
the  one  off  the  point  of  the  Hook.  And  he 
should  be  so  certain  of  that  shoulder  that  he 
could  take  a  departure  from  it  in  the  middle 
of  the  night  and  steer  boldly  for,  let  us  say, 
the  entrance  to  Block  Island  Sound.  How 
accurately  such  things  can  be  done  may  be 
illustrated  from  an  actual  case. 

Steaming  west  (in  squadron)  along  the 
south  shore  of  Long  Island  on  a  naval- 
militia  cruise  the  naval  officer  on  watch  on 
the  leading  ship  was  anxious  to  check  up  his 
course  by  a  bearing  of  Shinnecock  Light,  then 
miles  distant.  He  could  not  find  the  light, 
nor  could  the  lookout  at  the  masthead.  The 
naval-militia  officer  on  watch  was  an  experi- 
enced small-yacht  cruiser  and  knew  the  waters 
intimately.  He  asserted  that  he  recognized 
the  sky-line  of  the  land  and  was  certain 
that  the  ship  was  abreast  of  a  certain  village. 
He  went  to  the  chart,  laid  off  the  bearing  of 
Shinnecock  Light  from  the  calculated  position 
of  the  ship,  and  with  the  glasses  found  the  pin- 
point of  light  precisely  where  he  believed  it 
should  be  found. 

This  instance  serves  to  show  how  important 
a  knowledge  of  the  land  is  to  the  officer 
navigating. 


209 
LINES  OF   BEARING 

Particular  attention  may  be  called  here  to 
the  usefulness  of  lines  of  bearing  in  alongshore 
work.  This  matter  has  already  been  treated 
at  page  154  et  seq.  The  point  just  now  is  that 
a  small  coast-patrol  vessel  will  rarely  change 
her  latitude  so  much  that  a  new  latitude  ob- 
servation will  be  required.  If  you  are  any- 
where within  forty  miles  of  the  Ambrose 
Channel  lightship  you  may  assume  her  lati- 
tude to  be  yours. 

Now  you  can  find  on  any  clear  night  at 
least  one  conveniently  located  star  which 
will  give  you  a  good  line  of  bearing.  And 
you  have  only  one  chronometer  sight  to  work 
out.  Your  azimuth  gives  you  the  required 
line  of  bearing,  running  at  right  angles  to  the 
true  bearing  of  the  observed  star.  The  sun 
may  not  always  be  as  conveniently  located 
as  the  stars,  but  there  is  rarely  a  time  when  it 
cannot  be  advantageously  used  to  acquire 
some  information. 

At,  any  rate,  in  the  department  of  naviga- 
tion by  observation  there  is  no  other  method 
than  the  Sumner  with  a  single  line  which 
gives  useful  results  so  quickly  and  easily. 
The  coastwise  navigator  should,  therefore, 
make  himself  master  of  taking  azimuths  and 


210 

get  this  method  at  his  fingers'  ends.  An 
admirable  paragraph  in  Sturdy 's  Practical 
Aid  to  the  Navigator  is  pertinent  here: 

"After  having  been  for  some  time  without 
an  observation  and  any  body  sufficiently 
high  in  altitude  shows  itself,  take  its  altitude 
and  bearing  and  note  the  time.  The  ob- 
servation will  be  good  for  something — it  will 
give  you  either  latitude,  longitude,  or  a  line 
of  position,  any  one  of  which  will  put  you 
on  a  line,  and  show  the  relative  bearing  of  any 
land  that  may  be  near." 

COMPASS   AND  LEAD-LINE 

Perhaps  one  or  two  special  remarks  about 
the  compass  and  lead-line  in  the  more  or  less 
blind  navigation  of  war-time  along  a  coast 
may  not  be  amiss.  In  the  first  place,  officers 
must  impress  on  the  minds  of  all  members 
of  the  crew  that  they  must  not  go  near  the 
compasses  with  any  steel  on  their  persons.  I 
have  seen  a  ship's  standard  compass  thrown 
out  3  degrees  by  the  mere  act  of  a  naval- 
militiaman  peering  into  the  binnacle  while 
he  had  a  steel  gromet  in  his  cap.  A  knife 
in  the  pocket  may  do  quite  as  much  or  more. 
I  have  seen  a  regular  seaman  carefully  deposit 
a  six-inch  shell  at  the  foot  of  the  standard 


compass  binnacle  with  results  quite  puzzling 
to  the  navigating  officer  till  he  made  a  personal 
examination. 

Furthermore,  the  commanding  officer  of  a 
vessel  should  see  to  it  that  his  compass  is 
stationed  in  the  best  possible  place.  The 
builders  do  not  always  take  care  to  do  so. 
In  every  steel  or  iron  ship  there  is  a  neutral 
spot  where  deviations  are  reduced  to  the 
minimum.  Naturally  this  spot  is  most  fre- 
quently one  where  a  compass  cannot  be  put; 
but  it  is  worth  while  to  look  for  it.  You  may 
be  able  to  use  it. 

Do  not  allow  the  compass  to  be  placed 
where  shifting  steel  or  iron,  such  as  the 
topping-lift  of  a  boom  or  the  bolt  in  the  heel 
of  a  derrick,  is  near  it.  Every  change  of 
position  in  such  shifting  metal  will  alter  the 
deviation  of  the  compass.  And  it  will  not 
make  any  difference  what  stands  between  it 
and  the  compass.  Magnetism  will  operate 
through  anything,  even  a  stone  wall. 

If  your  compass  has  compensating  magnets 
see  that  they  are  inside  the  binnacle  box  and 
that  you  have  it  locked  and  the  key  in  your 
pocket.  Ignorant  members  of  the  crew  some- 
times find  the  binnacle  box  a  handy  place  to 
stow  a  pair  of  scissors  or  a  knife.  The  result 
is  compass  error.  Magnets  fastened  to  the 


212 

deck  outside  the  binnacle  box  are  likely  to  be 
moved  by  some  one  unacquainted  with  their 
importance.  In  the  kind  of  navigation  to  be 
done  alongshore  in  war-time,  and  especially 
in  the  frequent  fogs  of  our  summer,  or  at 
night,  the  compass  will  be  the  officer's  main- 
stay. He  must  needs  see  that  it  is  well 
guarded.  Next  to  that  will  come  the  lead. 
Of  course  the  type  of  craft  designed  for  patrol 
work,  especially  the  submarine-chasers,  draw 
very  little  water  and  will  seldom  be  in  danger 
of  grounding  except  when  very  close  inshore 
or  in  waters  dotted  with  "middle  grounds" 
and  other  traps. 

But  the  use  of  the  lead  in  ascertaining  the 
position  of  the  ship  will  be  frequent  and  in- 
valuable. This  matter  has  already  been 
fully  treated  (pp.  32,  47).  But  the  coast- 
patrol  officer  should  study  his  chart  till  it 
becomes  an  integral  part  of  his  information. 
He  should  be  able  to  get  some  information 
from  a  single  cast  and  more  from  a  series, 
even  on  the  thickest  night.  In  short,  he 
should  aim  at  resembling  the  New  England 
skipper  who  was  so  intimately  acquainted 
with  the  bottom  that  his  men  tried  to  play 
a  practical  joke  on  him  by  salting  the  lead 
one  night  with  a  bit  of  earth  brought  from 
the  home  port.  Whereupon  he  exclaimed: 


"Stop  the  ship!  We're  right  over  old  Marm 
Hackett's  garden." 

Soundings  on  the  Atlantic  coast  of  the 
United  States  are  of  a  nature  to  be  extremely 
useful  in  coastwise  navigation.  A  patrol  boat 
engaged  in  the  swift  and  arduous  business  of 
submarine-chasing  may  often  run  out  of  her 
reckoning  and  lack  opportunity  to  obtain  a 
good  fix  by  observation.  But  she  will  almost 
invariably  be  able  to  locate  herself  by  sound- 
ings. 

Of  -  course  small  patrol  boats  will  not  be 
equipped  with  deep-sea  sounding-machines. 
The  hand  lead  will  have  to  serve  them  and 
when  they  are  in  more  than  twenty  fathoms 
they  will  have  to  find  their  position  either  by 
observation  or  by  running  in  with  the  land 
till  within  twenty  fathoms. 

SIGNALING   AND  QUARTERMASTERS 

In  any  vessel  large  enough  to  rate  a  navi- 
gating officer  the  whole  business  of  signaling 
belongs  to  his  department.  The  navigator's 
division  includes  the  ship-control  crew,  the 
signal  crew,  and  the  radio  crew.  The  navi- 
gator's principal  non-commissioned  assistant 
is  the  chief  quartermaster,  who  should  have  a 
sufficient  knowledge  of  elementary  navigation 


214 

to  equip  him  for  his  post.  He  must  also  be 
fully  acquainted  with  all  the  Navy  methods 
of  signaling,  by  the  code  flags,  the  inter- 
national code  flags,  the  Ardois  lights,  flash- 
lights, and  wigwag. 

A  coast-patrol  boat  will,  of  course,  not  rate 
a  navigating  officer  nor  a  chief  quartermaster. 
The  duties  of  these  positions  will  fall  upon  the 
commanding  officer  and  such  petty  officer 
(quartermaster)  as  the  department  allows 
him.  In  fact  in  small  craft  handled  by 
small  crews  handy  men  will  have  to  be  in 
the  majority,  and  it  will  generally  be  a 
case  of  "all  hands  and  the  cook"  in  every 
watch. 

Officers  of  patrol  boats,  coast-guard  boats, 
etc.,  should  be  their  own  chief  quartermasters 
and  should  have  signaling  at  their  fingers' 
ends.  The  systems  will  be  found  concisely 
explained  in  the  Deck  and  Boat  Book  of  the 
Navy,  which  can  be  obtained  from  the 
United  States  Naval  Institute  at  Annapolis. 
They  are  also  to  be  found  in  the  Blue  Jacket's 
Manual,  likewise  published  by  this  institu- 
tion. Every  seaman  on  a  war-ship  is  now  re- 
quired to  know  how  to  send  and  receive  wig- 
wag. This  rule  should,  of  course,  apply  to 
officers  and  men  on  patrol  craft. 

It  need  hardly  be  added  that  every  officer 


215 

and  quartermaster  should  be  thoroughly  ac- 
quainted with  all  foreign  flags  and  uniforms. 

MINE-FIELDS 

In  war-time  harbors  are  mined  and  a  small 
channel  is  left  for  the  passage  of  vessels.  It 
is  the  duty  of  every  officer  to  acquaint  himself 
with  the  location  of  all  mine-fields.  Patrol- 
boat  officers  should  have  records  of  those  in 
their  districts  and  should  indicate  their  boun- 
daries on  their  charts. 

It  is  customary  to  detail  a  vessel  to  serve 
as  a  mine-field  guard  and  directions  given  by 
such  vessels  should  be  scrupulously  obeyed. 

Similar  rules  apply  to  harbor  entrances 
protected  by  steel  nets.  There  is  a  passage- 
\vay  through  every  such  net,  and  this  will  be 
indicated  to  properly  authorized  craft  by  the 
guard  vessel  on  duty  at  this  point.  No  boat 
should  attempt  to  pass  a  mine-field  or  a  net 
at  any  point  except  that  indicated. 

Merchant-vessels  of  neutral  nations  are 
usually  permitted  to  enter  mined  harbors  at 
stated  hours  and  to  depart  likewise  at  fixed 
times.  In  such  cases  they  are  customarily 
guided  by  the  patrol  boat  on  duty. 


THE   NAVAL   COAST-DEFENSE 
RESERVE 

This  is  the  branch  of  the  Naval  Reserve 
force  especially  needed  for  the  patrol  of  our 
coasts  to  detect  raiders,  submarines,  and 
other  craft.  It  includes  patrol  boats,  seamen 
and  officers  for  them,  civil,  structural,  and 
mechanical  engineers,  and  all  others  who 
can  be  utilized.  Lieut.  R.  F.  Barnard,  U.S.N., 
has  prepared  a  pamphlet  giving  information 
on  this  subject.  It  can  be  obtained  at  the 
office  of  the  Naval  Training  Association  of 
the  United  States,  26  Cortlandt  Street,  New 
York,  or  42  Water  Street,  Boston. 

The  plan  calls  for  seven  hundred  and  fifty 
boats  and  ten  thousand  men  to  patrol  the 
third  district  alone,  comprising  the  waters 
from  Barnegat,  New  Jersey,  to  New  London. 
Small  motor-boats  to  operate  close  to  shore, 
larger  ones  to  work  farther  out,  and  coast- 
guard vessels,  tugs,  large  yachts,  etc.,  to  be 
on  the  outer  line  as  scouts  and  to  act  as  con-  , 
voys  for  merchant-vessels  are  to  be  used. 
The  pamphlet  says : 

44  A  patrol-boat  unit,  as  we  call  it,  for  small 


217 

boats,  say,  forty  feet,  would  be  one  ensign, 
one  quartermaster,  one  engineer,  and  four 
seamen.  Two  members  of  that  unit  must 
be  experienced  to  some  extent;  they  are  the 
ensign  and  the  engineer.  Unless  you  have  an 
engineer  who  can  handle  your  engines  prop- 
erly you  might  just  as  well  anchor  your  patrol 
boat  and  stay  there.  The  ensign  has  got  to 
be  familiar  with  coastwise  navigation,  know 
how  to  read  charts,  how  to  fix  cross  bearings, 
etc.  He  should  not  have  gotten  his  knowl- 
edge out  of  books  entirely,  but  by  kicking 
around  on  boats ;  in  other  words,  he  should  be 
a  yachtsman,  a  good  fisherman,  or  something 
like  that,  but  so  far  as  the  other  men  in  that 
unit  are  concerned,  they  need  have  had  no 
previous  experience.  If  we  only  enrolled  as 
quartermasters  in  this  Naval  Reserve  men 
who  know  how  to  signal,  we  would  have  very 
few  quartermasters.  We  take  them  on  faith, 
hoping  they  will  learn  and  learn  quickly. 

"The  same  thing  applies  in  regard  to  sea- 
men. The  first  thing  that  we  want  them  to 
study  is  ordnance,  especially  the  small  guns, 
such  as  one-pounders,  three-pounders,  six- 
pounders,  and  machine-guns.  Then  after 
that  we  will  want  the  seamen  also  to  learn 
signaling.  The  ensign  has  got  a  whole  lot  to 
learn.  He  ought  to  know  something  about 


218 

naval  regulations;  something  about  limits 
of  submarines;  something  about  scouting; 
something  about  mines  and  mine-sweeping; 
and  should  inform  himself  as  to  deep-sea 
navigation,  if  practicable.  Any  member  of 
these  units  has  got  enough  work  to  last  him 
for  a  long  time,  but  you  have  got  to  have 
instruction,  some  from  studying,  and  some 
from  experience,  and  the  best  way  to  get  this 
practical  experience  is  to  enroll  in  this  Re- 
serve and  let  us  direct  your  course  of  study." 
One  of  the  attractive  features  of  this 
service  is  that  it  permits  a  yachtsman  to 
organize  his  own  crew  from  among  his  friends 
and  enroll  together.  This  service  should  ap- 
peal with  great  force  to  yachting-men,  power- 
boat owners,  and  former  naval-militiamen. 
There  is  plenty  to  do  and  the  need  of  men  and 
boats  will  always  be  great.  When  there  is  no 
war,  a  man  can  resign  if  he  wishes  to,  or  remain 
subject  to  call. 


THE    END 


UNI 

BERKELEY 

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